I could do that. I'm not up to date on the whole DS format, do DS Lite and 3DS share the same games? What's a DS Lite anyway? I should research all of this.
EDIT: Ok I did some reading on Wikipedia. So with a DS Lite I can still play GBA games. That rocks. DSi and 3DS don't have GBA slots. That sucks. So it sounds like DS Lite is the way to go for me.
DS Lite can't play 3DS games. It's basically the previous generation of Nintendo handhelds. DSi is in the same generation, though it does lack the GBA slot. But since it's older, you can get a refurbished one pretty cheap and still look around for various other games. DS Lite can play the fourth gen AND fifth gen pokemon games:
Diamond/Pearl, Platinum
Heart Gold/Soul Silver (gen 2 remakes)
Black/White, Black2/White2
Plus you should be able to find various other games that would interest you, e.g. Zelda: Phantom Hourglass, Zelda: Spirit Tracks.