Other than cheap kids bikes, I've never worked on a BB before. Almost everything else, but no BB experience. I read up on it last night in my book. The book shows 2 spanners, and a special wrench to remove the outer nut/retainer. (I know not all bb's are the same.)
Anyway, one of my bikes definitely needs BB work, and another needs some PM.
Do I need those special spanners and wrenches? I've got plenty of basic tools like wrenches, etc.
If so, what would you all recommend? I prefer to do my own work whenever possible. I'm sure you all understand.
Thanks in advance.

Having the right tools will certainly make your repairs easier to do and less frustrating. May I suggest taking a look at the Park Tool web site and see what tools would match your needs: https://www.parktool.com/

You can get by without them but, as it sounds like to plan to keep these bikes around for a while, it would be a good investment to buy the right tools. Just buy the ones you need when you need them and you'll eventually build up a great tool kit.

...and what tools you will need depends on what kind of BB your bike has.

The loose ball BB's have some tools in common, some variation, like lock ring and the adjustable race on the left side.
many additional types of BB mechs have come out since, each with their own tool requirements .

Whatever you do, do not hack up the BB with the wrong tools..... The correct tools are fairly inexpensive, and will make the job at hand much more simple, and you will have them for next time.

With over 1400 posts to your credit here at BF's I'm going to assume that you're an avid enough cyclist to have a bike or bikes that are a cut above using bikes with cup and cone style BB's. Far more likely your bike has a sealed cartridge style BB. It may be square taper or one of the newer spline styles. You'll need to study your bike's BB area to figure out which you have and then buy the tools accordingly.

I'm not an advocate of buying every tool under the sun but bottom brackets, like freewheels, require special tools. Depending on the vintage and type of BB system you'll need a splined remover (no way around that) or a pin spanner, lockring tool, and fixed cup wrench. There's some wiggle room on the three tools for older cup and cone BB's, but not much.