Well, let me answer a few of your questions, to the best of my knowledge (I'm mostly a NES collector lol)
There's several versions, and I believe this site can explain them the best:
http://www.atariage.com/2600/archives/consoles.html
I'm not sure on this one. (Translation: /me waits for a 5200 collector/expert to show up.)
As far as I know, the 7800 cannot play Tigervision's games, so no Miner 2049er, and it cannot play Pitfall II because of it's extra hardware (I think). Pitfall II included an extra chip so it could have music and I believe that's where the 7800 incompatabilities lie.
Again, see the site that I pointed out. That page explains all the system variants and what they output, though I believe most, if not all Atari systems output RF.
I've always preferred the 2600's controller. The 5200 controller is prone to breaking and the 7800's controller has always felt uncomfortable to me. That being said all 3 are usable controllers. I guess you'd have to try each one and decide which one you like the best.
For the 7800 there's Food Fight and Ninja Golf. Dunno about the 5200. I guess there's probably some more great 7800 and 5200 games but those are the ones that instantly come to mind.