If you're handy doing things, which it sounds like you are, go for it. I feel like there's this huge taboo about taking apart lenses. It really isn't rocket science for most vintage primes. As mentioned, you need to get a good JIS screwdriver set, but also have whatever jewelers set you can get your hands on, because you will find some drivers from one set will just fit whatever better. In addition to the spanners mentioned, you will also want to get tools to remove the front rings, which is often your entry point. I've had good luck with this set:
amazon.com : 18 Sizes Lens Tool / Filter Wrench Set Rubber 37mm 43mm 49mm 52mm 55mm 58mm 62mm 67mm 72mm 77mm 82mm 86mm etc : Camera Lens Accessories : Camera & Photo?tag=pentaxforums-20&
A 50/50 mixture of ammonia and hydrogen peroxide is often recommended for fungus removal. Here are some links. The first is short and sweet and is focused on the optics specifically. The second ones gets into the whole disassembly etc.:
Fungus: how to prevent growth and remove it from optical components How to Remove Fungus from a Lens
If you do get into something like a zoom that slides and rotates, do make a drawing of the pieces. Yeah, guess you could photograph, but I like sketching it out on a piece of paper that sits there for disassembly and reassembly. I think you learn the pieces better that way, and no batteries required
I did a vintage Vivitar Series One that was a twist and pull, and went as far as laying down some of the bushings on the paper within outlines I drew matching the cutouts on the barrel. The differences between some of the nylon bushes and associated screws were very subtle. Something with motion like that can get complex, so care is needed.
Also, you'll find strategic dabs of what's probably lacquer (as always, someone correct me if wrong) on retaining rings and sometimes screws. I've been able to dissolve these with Q-tips wet with rubbing alcohol held on them.
When unscrewing the last bit of a focus assembly, pay particular attention to the alignment of the pieces. This can save lots of time getting pieces lined back up right for infinity focus etc.
I got into the fungus removal business from an 8 element Takumar 50 I bought on a Goodwill auction. After that, I've had a variety of others come my way. While I would only buy one on purpose for the right price, I'm no longer horrified by the prospect. Fungus can etch the glass or coatings, so you have no idea until you go to clean it what will happen.