yeah, I remember when I first got my old GBA. I bought with an import copy of Super SFII X Revival since that was the only game I really cared to see when the GBA first came out. At the time, I considered it the best handheld fighter (more like the original than any other, but NGPC ones were still more fun).
I didn't get many more games for it until much later and now I've amassed some 40 or so games. Out of what I have, I'd highly recommend:
All Golden Suns (best portable RPGs, I think)
All Castlevanias
All Metroids
All Kirbys
All Final Fantasys
All Zeldas
F-Zero (as good as the SNES version!)
Boktai (i think there's a second one but I don't have it)
The KoFs
Super SFII Turbo Revival
Drill Dozer
Mario Kart
Galaxian Galaxies
The different Mario remakes (most are worth it)
And if you can still find them cheap:
The Spyro games (they were surprisingly fun, but easy)
SSX Tricky (not too bad of a port, but kinda easy)
SF Alpha 3
Lunar Legend (interesting remake of the original)
Jet Grind Radio (again, not a bad portable port)
The different Sonic titles (I had the first one which kinda sucked, but I heard the other two were better)
As for mapping the shoulder buttons to X/Y, I thought I had heard of a mod to do that on the DS, but I may just be thinking of the old GBA mod that added two buttons above A and B which were the same as L and R. Seems like you could probably develop a mod like that, though. Maybe just have a switch on the side or something to switch between X/Y mode and L/R. A lot of work to go through for something like that, though
Personally, I'd like to see a mod to let me play my GB and GBC games on my DS.