I recommend the Gamecube with GBA player (it's an add-on but a great one for about $20). The GC has quite a few arcade compilations (Namco collection has all the Pac-Man's) and you can get your puzzle fix from both the GC and GB/GBA library (which is huge by the way). It has some great sports games like the great 2005 Madden, Sega Soccer Slam, and all the other sports franchises that get updated every year but are basically the same game. Also, you can play all 2D Mario's (and Zelda's) through the GBA player.I use to own a NES many years back, so I will likely not make that my first choice. I'm leaning towards a PS, but that's up in the air. Here's my interests...
-puzzle and sports games especially
-classic games ('80s, Ms. Pac Man, Mario, etc.)
-low cost system with little if any add-ons
Cheap? Yep, you can go out today and pick one up at Gamestop for $30. Just make sure that you get them to open up the box and examine it for yourself. Look for a clean one (I like the black one but color's up to you) and make sure it has a Nintendo brand controller included with it. You'll also probably be able to find several cheap titles there.
I would also recommend the Wii but their download policy sucks. Buy carts and discs and you won't regret it.

