For 3DS shooters, Kid Icarus: Uprising is an obvious choice. Possibly the best game on the platform, and one of my favorite shooters on any platform. Resident Evil: Revelations is also very good, though you may want to wait for the console versions this May. Star Fox 64 3D is supposed to be great but short. If you're open to 2D side scrolling games like Mega Man, try Gunman Clive and Mutant Mudds.
As for JRPGs on the 3DS, the best choice available seems to be Fire Emblem: Awakening. I, however, can not personally attest to its quality. I can, however, tell you first hand about a couple of other good games. Paper Mario: Sticker Star is not the best JRPG ever, but its Item-based combat is a surprisingly meaty novelty. Kingdom Hearts 3D is the best action RPG on the system, despite a convoluted story and one or two awkward mechanics. Theatrhythm: Final Fantasy is a Music/JRPG hybrid, that plays like Guitar Hero or Elite Beat Agents, but has the leveling up, items, and characters of an RPG. And if you like Fire Emblem, try out Devil Survivor: Overclocked, a Shin Megami Tensei interpretation of the SRPG, and Ghost Recon: Shadow Wars, essentially a Western made modern Fire Emblem.
As for Vita games... I don't own a Vita. But these other people seem to have good advice.