One thing I remember from my early childhood is that I had an uncle who had an NES system with Legend of Zelda 2 and Super Mario Bros 3. I was a pretty lucky kid who had a Super Nintendo and a Nintendo 64, but I loved going to my uncle's house to play on the older system.
Definitely get a Wii. The best part about is the backwards compatibility with Gamecube games. You have two generations worth of Nintendo games to play with.
For the Gamecube, I recommend Mario Kart Double Dash, Animal Crossing, and WarioWare, Inc.: Mega Party Game$!.
For the Wii, I recommend Super Mario Galaxy, WarioWare: Smooth Moves, and Punch-Out!!