Whatever you do, consider your personal safety first.
The risks for your health, that you take by ignoring the next lines, do not worth it.

Abandon lead-based and cadmium-based solder and components completely.
This is usually the main source of contamination in a lab. Throw away (recycle) all your lead-based or cadmium-lead-based (woods metal etc.) solder immediately and obtain lead-free solder. Both lead and cadmium are toxic. I know, lead-free solder is much more expensive and I also know that lead-free solder may not always give shiny solder joints, but with care and practice you will learn how to make good solder joints using lead-free solder too. The risk you take from lead or cadmium contamination does not worth it at all and it may be serious! The lead-free solder alloy you should look for, is the SAC305 (Sn=96.5%, Ag=3%, Cu=0.5% or similar ratios) or the SnCx plus 07 (Sn=99.3%, Cu=0.7%) or similar solder alloys. According to Wikipedia, Sn, the main metal in this type of solder, is non-toxic. Ag and Cu, in such low quantities should not be considered to my view as a significant health hazard. After all, people wear silver rings and copper is all around us in the coins or in bronze alloys. In fact the SnCx alloys may be even safer as they do not contain any Ag. I would also avoid lead-free solder that contains significant amounts of Sb or Bs elements. However, even if using lead-free solder, I recommend to wash up your hands after any soldering activity, before touching any door knobs or other home surfaces that other people might use, to limit the metals exposure to your family members. Also avoid breathing the fumes or the hot air just above the iron, use some means of room ventilation. Don't forget, that even lead-free solder do contain lead and other metals, mainly as impurities (very low amounts in the class of 0.xx%). After you abandon lead-based solder, make sure you thoroughly clean the area that you think it has been contaminated with lead previously. This includes the workbench, the measuring equipment knobs, the soldering iron tip (even replace it if you get too extreme), the door handles/knobs in your laboratory and possibly all the door handles in your house. Even with lead-free soldering, make sure you regularly clean up the workbench. Do not use the house vaccuum cleaner at any instance to suck in the garbage and there is a reason for not doing so. Use wet handkerchiefs or baby wipes to make the tiny dirt stick into them and and throw them away after cleaning. The same process is used to drag away mercury droplets if a fluorescent lamp is accidentally broken, use wet handkerchiefs or baby wipes only. Also make sure you throw away (or donate with warning notice) all your previously lead-soldered failed projects and any lead-soldered PCBs taken out from old equipment for parts. A project that is completed and enclosed in an enclosure do not harm, but a failed project PCB soldered with lead-based solder and hanging around your workbench, will eventually cause lead contamination problems. Note, that even if you abandon lead-based solder, some of your components may still contain lead onto their pins, if they are not ROHS. Now, I do not suggest throwing away all your components, but by just throwing away lead-based solder, you minimize lead contamination at a great amount. Another source of lead or cadmium are these die cast project enclosures, as they do contain some amount of lead and cadmium, although the percentage is very small. Cadmium, is also contained in these BIOS batteries of very old PC motherboards (486-386 and prior), which usually leak. Another source of cadmium, are many old tube radios and equipment, as many of them have cadmium-plated chassis and other parts. Especially if this cadmium-plated chassis starts to rust (giving mostly a yellow-ish or white-ish dusty finish) these dust particles can end in your lungs, which is the worst place to be. If you are very cautious about safety, you should consider abandon such equipment as well, especially if it leaks or rusts.

Do not breathe the solder smoke fumes.
Do not breathe the solder smoke, especially if you solder for a few hours a day. Build a small homemade ventilation system, or open the lab windows if that is possible. Whatever you decide to do, the idea is to move the solder smoke away from your face and take it outside the house somehow. It is not only the resign that evaporates that might cause problems, but also microscopic metal particles from the solder, that may be released into the air, although this last part is ambiguous.

Do not breath fumes, smells or micro particles from any other chemical or material.
Cleaning, PCB etching and other chemicals fumes, even if they do not smell, can be dangerous. They must be taken out of the home. You can use the same ventilation system you have build for the solder smoke fumes to take them out, or just ventilate your lab by openning the windows regularly. During the work, micro particles from PCB or metal chassis drilling and other such activities, can be usually sucked using a vacuum cleaner, without exhausting them out of the house. However, fumes and vapors cannot. Note, that some enameled copper wires used on coils, can produce highly toxic fumes when the enamel paint is stripped away by burning it with the soldering iron. Some old military gear, contains electronics coatings that are extremely toxic (like Trichlorotrifluoroethane) if one inhales their chips or burn them. It is usually mentioned in the technical datasheets, be warned about this.

Do not handle beryllium or radioactive material containing products.
Many high frequency transistors (usually the white ceramic power transistors used in amplifiers), hybrid modules and connectors, contain beryllium alloys or beryllium oxide bases, to transfer the heat more effectively to the heat sink or to add rigidness. Oven magnetrons (their top ceramic tip) and other high temperature electronics may also contain beryllium oxide insulators. Beryllium and especially beryllium oxide, is highly toxic when its dust particles are inhaled. It is not always noted on a datasheet if a product contains beryllium oxide, so be very careful. I believe most of these planar (crossed golden sheet pins) RF power transistors enclosed on ceramic or plastic case contain beryllium oxide. Some old Phillips datasheets, warn about this, but most others don't. Some plastic RF power transistors in TO-220 cases may do so as well, but they are way much harder to break so they do not present a risk. Note that Beryllium coper is used in many good quality RF connectors, as well as springy sockets and contacts. The Beryllium percentage in these, is usually relatively low, so as long as you do not grind or cut these, you should be safe. Dont mess with these componets, leave them alone.
Radioactivity is even more dangerous. Some special electronics components, like T/R radar tubes, some old fire sensors and gas regulator tubes contain radioactive materials. You can see some examples of tubes that do contain such materials, at the appendix at the end of this page. Many power triode tubes contain thorium coated cathodes (alpha emitters). As long as you do not break the tubes, you are safe, so do not break them. Many older power tubes contain Uranium glass in their pin sealings, that can be identified by its green glass color. I am not sure how dangerous these are to handle. Old military equipment does have components that contain radioactive Radium paint, a very nasty stuff. These components are panel meters (a good example is the meters of the R390A), panel markings and knobs markings. Since you do not have a means of detecting these materials, to be safe in case of handling or worse breaking them, I would suggest you to carefully throw away (recycle) all these products. If you do not want to go that extreme, buy a geiger counter that is capable of detecting gamma, beta AND alpha particles. Radium radiates mostly alpha particles and you wont be able to detect much of its radioactivity with a cheap geiger counter that detects gamma and beta radiation only.

Abandon mercury-containing bulbs and products.
Mercury, another source of serious contamination, is used extensively on Fluorescent Lamps, Compact Fluorescent Lamps, Cold Cathode Fluorescent Lamps, some special relays and switches or special lamps for UV production, such like the ones for printing PCBs. Mercury will possibly not found exposed in the lab, but the problem begins when such devices are broken. Some times, it is very easy to brake them, especially if you keep them around without a protective enclosure or if they accidentally drop. Unlike other metals, Mercury is liquid and it is very difficult to clean it up when it is exposed. In case of a broken mercury bulb, remember, do not use the house vaccuum cleaner at any instance to suck in the mercury containing garbage and there is a reason for not doing so. Use one-time-use gloves and wet handkerchiefs to make the tiny dirt and mercury droplets stick into them and and throw them away (and the gloves) after cleaning. You really might have to throw away other useful things that are contaminated with Mercury, to avoid further LAB contamination, even your clothes in extreme cases! Thus it might not be a bad idea to throw away (recycle) at first these devices, before disaster happens, and try to replace the bulbs in the lab with other types, incandescent, LED and halogen. Not only these make a better light, but they also do not emit serious amounts of UV (some halogen lamps have a UV-stop glass or else, external UV-stop filters must be used with these). Technology has been improved over the years and now you should be able to afford good quality LED bulbs as well, which are also power friendly.

Wear protective glasses at all times.
You never know when melted solder, hot resign droplets or even the soldering iron tip will end up onto your eyes. Also, any liquid chemical will eventually accidentally thrown onto your eyes. So wear protective glasses whatever you do. Doing a small mistake or ignoring the danger, can seriously harm your eyes, or make you totally blind. Does it worth it? Do not say "I am careful, it won't happen to me", eventually it will! Listen to people with previous experience on this.

Wear protective glasses, gloves and earplugs on all mechanical work.
With every screw, spring or micro mechanical particle you turn/push/pull, there is a highly potential danger of it to be thrown away to your eyes. Broken razor cutters and drills are very common examples of how a part can easily end up to your eyes. This is very serious and it can blind you instantly, so wear protective glasses! Like explained before, do not say "I am careful, it won't happen to me", eventually it will! When dealing with chemicals, always wear additionally gloves. When dealing with heavy machinery like hammers, lathes, drills, electric cutters etc., always wear glasses, gloves and earplugs and keep your hands as away as possible from their moving parts. Apart from reducing the harmful noise on your ears, earplugs will help you concentrate more to the task you do and concentration is very important to avoid accidents that can severely injure you or even kill you.
 

Take care when you work with high voltages or high currents
If you are reading this page, you already know that you have to be very careful when working with anything that uses high voltage or high current. An example of high current is the electric welding machine and examples of high voltage and/or high current are machines like CRTs, most vacuum tubes and tube audio amplifiers, high voltage power supplies, high voltage capacitors, X-ray machines, special high voltage experiments etc. Depending on the voltage and current, you have to obtain special insulating gloves and it is always a good idea to discharge the high voltage capacitors and use insulated tools to touch and work with these parts. Also note that some special high voltage tubes, when operated at many kilovolts, will produce amounts of X-ray radiation, which can be lethal and not easily detected without the proper detection equipment.

Ventilate your lab regularly
Air purity is important in the lab and everywhere else. Take action to ventilate regularly your lab. This may be every time you enter the lab or at other times during the day. All the equipment and machinery is composed of plastics, paints, grease and a whole lot of other chemicals that are not health-friendly. Especially if your lab is located in a basement (but not only), you have to take care of the radioactive Radon gas, that comes out from the ground or produced from the building materials. A simple Radon gas detector can notify you for the contamination of air from Radon. All the above problems are solved by ventilating your lab regularly. This can be simply done by opening the windows regularly, or by installing a ventilation system, which is more expensive though.

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Appendix: List of British manufactured joint service valves which may be radioactive - dated March 1961.

(note the symbol 'c' as published is an older symbol for the 'curie', now Ci)

* CV2248 to CV2252 inclusive, CV2374, CV2375 and CV5229 made before April 1961 contain Radium Bromide.

List of American manufactured British joint service radioactive valves showing British CV numbers and American tube types - March 1961. Note the information in Columns 3, 4 and 5 is extracted from SSC.347.

Joint Services specification K1001 indicates that valves would not come into the radioactive class if they had less than a given amount as indicated in column 2 below. If a valve had more than one substance then provided the total did not exceed those in the table it still would not come into the radioactive class. E.g. if a valve had 0.8 microcuries of Krypton 85 then it has 80% of the permitted amount of that element. If it also contained 0.02 microcuries of Caesium 137 this would represent 20% of the permitted amount. Added together this is 100% and thus still within the total limit. In all cases the maximum permitted radiation dose rate allowed at surface of valve in millirads per hour was 0.01.