First off, if you're using emulators, let me introduce you to RetroAchievements.org in case you want achievements for your classics.

Golden Sun is an absolute classic RPG, but it's a not investigative. Pokémon is always a classic, and if you want a new experience, ROM hacks are plentiful. Final Fantasy I & II: Dawn of Souls is an updated version of FF 1 and 2. Super Mario Advance is pretty much Super Mario World on GBA. Final Fantasy Tactics Advance was great if you like turn based tactics RPGs, and it's a DIFFERENT game from FF Tactics on PSX, it is NOT a remake or port. Legend of Zelda: A Link to the Past is a port of the SNES classic. I'm sure I'm missing some classics, but those are what I can remember and personally played. And all should have achievement support on RA.