The 7800 plays (almost all) 2600 games, as you've figured out. The 5200 is its own beast -- though the 8-bit Atari computers are essentially 5200s with built-in keyboards and smaller cartridge slots. The 5200 also has terrible joysticks, apparently. For all three, not only do you require a PAL console, you also can only play PAL-specific games on a PAL TV.
Really, there weren't all that many 7800 games worth playing, so you may be better off just getting a (probably much cheaper) 2600. (Although the 7800 does boast Ninja Golf, which is definitely worth playing.)