Tomodachi Life

Witcher 3 seems to be the thing of the moment. ( ͡° ͜ʖ ͡°)

Ace Attorney (Phoenix Wright) series.
Pokémon OR/AS is a good choice too, though. Or Pokémon X/Y.

Fantasy Life It's an RPG Sim game.

Then there is Rune Factory 4 which is really fun and it's like Moon Harvest, but with combat in it rather then just farming.

Omega Ruby is awesome pokemon game

Fire Emblem Awakening is a good game that allows you to customize your own character

There are more, but those are the top ones I can think of at the moment.

For multiplayer Experience i recommend getting:Monster hunter 4G,Mario Kart 7,Super smash Bros.
Adventure: Pokemon X/Y,The Legend Of Zelda: A link Between Worlds (Game of the year),Super mario 3D,Resident evil Revelations, animal Crossing new leaf

Monster Hunter is the best 3ds game in my opinion. I would also strongly recommend a zelda game, kid icarus is apparently a very hard 2d platformer which people love, Rune factory is the new harvest moon king atm. Rpg Wise I enjoyed Fire Emblem, or an odyssey game.

Check if there are not any promo actions. Around Christmas I've bought 3DS + Pokémon Omega Ruby and got Legend Of Zelda: A link Between Worlds (six games to choose from) for free.

I really liked Kirby Triple Deluxe. You should check that out. Kirby games are always... "happy"

Buy a 3DSXL because is way better than the normal 3DS (i still play on normal because have the special edition of Ocarina of Time, only because of that). You can download two free Pokemon games (Shuffle and Rumble) that you will play everyday for a long time so don't worry with Pokemon, still when you get a full game between X/Y and Shapphire/Ruby in my experience i got every single pokemon in X and i still didn't finish Shapphire. It's a remake of a great game but i don't know, i don't feel the game like X. But ofc we are talking about you and i can recognize that Shapphire/Ruby are better games with a lot of new stuff and you should go for one of these since you didn't play the other ones.
If you like Pokemon that should be without doubt what you should start to buy because you have hundreds of hours like you know and if you want to get in meta you have a whole new community to know.

To start i would buy a Pokemon game and a Super Mario (try to see if there is for example Super Mario 3D Land used).
Other games that i love on 3DS:
Fire Emblem: Awakening
The Legend of Zelda: A Link Between Worlds
Kingdom Hearts 3D: Dream Drop Distance
Animal Crossing: New Leaf
Bravely Default
Xenoblade Chronicles 3D
Professor Layton and the Miracle Mask
Theatrhythm Final Fantasy:

Then ofc you have Phoenix games, Shin Megami Tensei Mario, Super Smash, Luigi, Donkey Kong... So many stuff. I could say a lot about them but in the end is about personal taste. For example, One Piece games aren't great but i enjoy since i'm a big fan of the serie.

Shin megami tensei

Super mario 3d land is amazing, as well as animal crossing and street fighter 4.

Harvest Moon

Zero Escape: Virtue's Last Reward
Pokémon Mystery Dungeon: Gates to Infinity

SUPPA

SMASHA

BROTHARS

I can't recommend 999 and Virtue's Last Reward enough.

The Professor Layton Series (DS-3DS)

Super Smash Bros, because you can't have a Nintendo console without Smash!

Buy Kid Icarus Uprising. My favorite game of all time.

Also, Elite Beat Agents is an old DS game that's like 5 bucks at Gamestop and it's totally worth the money.

I've had Animal Crossing: New Leaf since it came out and I still play sometimes. If it's your type of game(simulation I think) you can get a lot of game play time from it.

I'd go with Pokemon Omega Ruby or Alpha Sapphire. These titles feel more like a hybrid of Final Fantasy and the older Pokemon titles considering their design.
GameFreak tends to fix quite a few minor flaws with each main game they release and, in this case as well, there are improvements compared to X/Y. Personally, I prefer ORAS to XY, but there's a lot of people that think otherwise - a matter of preference.
Choosing between Omega Ruby or Alpha Sapphire comes down only to which team you want to go against in the main story - the version exclusive Pokemon aren't really a factor, since trading has become really easy with access to the GTS.
The game was really enjoyable for me, though you need to remember a few things - mainly to disable the Exp Share item when you get it. It ruined my XY playthrough by overleveling my team.

I recommend Etrian Odyssey IV, tons of fun, but be prepared to grind a lot. You cannot go wrong with any Pokemon game or Monster Hunter 4.