i can figure out well enough what kind of razor to get...
I can't. Anyone care to help?
Edit: That said, I'm having a blast with classicshaving.com.
Edit 2: Will perusing local antique shops do me any good?
I've used Thiers-Issard razors bought new from Classicshaving with great success and highly recommend them. I did it the hard way and bought them without using the sharpening service from Classicshaving and just learned on my own. It takes longer that way because I didn't know if any shaving difficulties I was having were due to my poor (initial) technique or due to an incorrectly sharpened blade.
The easiest way to get a good blade to start with would be to buy a new one from Classicshaving and also purchase their sharpening service on that new blade. Thiers-Issard advertises their blades as 'shave ready' but the three I've bought were not ready without a small amount of honing and stropping. The Dovo blades are highly regarded as well and cost about the same as the TI blades. I think as long as you stick to one of those two then pick whatever blade works for your budget you'll get a good blade. Don't stress over the 5/8 size vs 6/8 or 7/8; when you're starting out it won't matter much because you'll be more concerned with shaving technique, just get whatever appeals from TI or Dovo (assuming you want new).
There are a number of other good blade manufacturers (and some "new old-stock" as well) that are great too. You can check out the recommended sources from Straightrazorplace and they'll be good too. Some members on Straightrazorplace will sell used blades that are "shave ready" and I've heard good things about those but never actually bought one. Those blades will be a bit cheaper than Classicshaving, maybe $40 - $60.
Regarding antique shops (and ebay): Pulling numbers out of the air, I'd guess 90% of those blades will be unuseable, either due to oversharpening or nicks in the edge, or warping, or poor heat treatment of the steel, etc. There are also a lot of Pakistani copies of real blades and they uniformly use cheap steel with poor heat treatment. If they take an edge at all it won't stay sharp long enough to complete even one shaving stroke. I went through a couple of those and it was a waste of time and effort. Once you have sharpened a few on your own you can pick out used ones with more confidence (although I've still been burned by poor heat treatment a couple of times and that won't show up on a visual inspection...).
The blade edge is amazingly fragile, and you'll become very protective of it once you get one shaving well. You have to start with a good manufacturer, that has been properly heat treated, honed correctly, and then stropped correctly. Lots of things have to be in balance and work together to get it to shave well. That's the appeal of the hobby!
If all of that is good, then the blade will glide over your face with no pulling at all and leave behind a freshly mowed patch that is glassy smooth. The critical test is shaving against the grain -- if the blade is smooth shaving against the grain then you're really got it sharp! But it's very frustrating to learn to sharpen a blade at the same time that you're learning to shave too; I almost quit several times.
I think it would be more rewarding to get a properly honed/sharpened blade from one of the "honemeisters" on Straightrazorplace and use that for initial shaving practice. Then buy a second used one or new one for your own sharpening practice and compare it to the shaving "feel" of your first one. That way you have something to compare your sharpening progress against.
Have fun and go slow!