Aside from the obvious vote for Fire Emblem,
Etrian Odyssey IV: Legends of the Titan gets my highest recommendation as an RPG. It's the easiest game in the series, but it's by far the cleanest to get into and you've got a lot of freedom.
Go buy 999: Nine Hours, Nine Persons, Nine Doors for the DS, play the hell out of that, and then hunt down Zero Escape: Virtue's Last Reward. One of the greatest gaming experiences I've had in a long time, but the first game is basically a requirement if you want feels in the last part of the game.
Professor Layton in the Miracle Mask is the fifth game in the series, but it's actually probably the easiest one to get into. Sure, the plot's insane - all Layton plots are - but the feels are there, and this one manages to not be depressing! Also, there are over 500 puzzles if you connect to Wi-Fi, so that's nice. Also, in terms of Layton games, Unwound Future (3) > Miracle Mask (5) > Diabolical Box (2) > Curious Village (1) > Last Specter (4), but Last Specter's good for backstory and Unwound Future needs to be played last if possible.