Well, first off, buy Namco Museum for the DS or GameCube. Play some of the classics and learn the twists. Then, move on to Sonic Mega Collection and give all four Genesis Sonic titles a shot. There's several options for the Super Mario games, Advance, Wii, and elsewhere, so you're probably set there.
Try out some arcade brawlers with friends if you get the chance. TMNT, TMNT: Turtles in Time are great examples, though you really can't find either without having to unlock them in some terrible Cube games at the moment.
Follow this up with some Shmups if you can. Chances are you won't find any of those easily available. I think Raiden III came out on the PS2, but I have no idea how traditional it plays.
Buy Super Metroid on the virtual console. I see you hate DRM, but for this game, it's worth it.
Final Fantasy VI Advance would be another top investment as well.
Those are off the top of my head as viable options, and most don't require the Wii. Good luck!