I'd have to say a Nintendo DS.
The graphics aren't the best, but they are decent and when you're playing a game the graphics really don't hinder the experience.
As for the game to go with it, I'd recommend Animal Crossing: Wild World or Mario Kart. They're both great and yet completely different. AC doesn't require much skill, it's a relaxing game and there's always something to do. Also if you know anyone else with wi-fi and AC:WW then the experience is even better. Mario Kart is fun, it's much more like the traditional games (in comparison to Double Dash!!), it's easily the best MK imo.
Since you like so many Sonic games you could also try Sonic Rush. It's a good experience and one of my favorite Sonic titles to date. It maintains the traditional left scrolling while adding new concepts such as tricks & a combo of 2D/3D.