3DS
Pokemon Platinum
Fire Emblem Fates
Ouendan 2
This was really tough. Mario Kart DS and Smash 4 were really hard cuts, but I already played MKDS to the point where I'm not sure if I'd be able to find much new in it (whereas I can't say that about the other three), and while I love Smash 4 I think playing it would just make me miss playing Melee (or really any Smash game properly with a Gamecube controller). Which game in each specific series was also really hard; Sun and Platinum are tied with Sun probably edging out Platinum, but I went with Platinum because I prefer its postgame. EBA/Ouendan 2 are similar with EBA being the game I prefer by a slight margin, but I went with Ouendan 2 because I think I played it a little less and because I prefer the music in it (and I wouldn't have as much music to listen to there).
There are also some games that don't really rank up with these but are still great and would be perfect for this setup, like Tetris DS/Party Deluxe, Animal Crossing New Leaf, and any of the WarioWare games.