I will make a list according to what I think you like. I will put numbers just to show you which game you should buy first.
RPGs/Tactics:
1°-The World Ends With You (I actually prefer DQIV but I think you will prefer TWEWY because of your avatar. It's an incredible game with unique gameplay and storyline. The gameplay is confusing when you play the game for the first time, but it's not hard)
2°-Dragon Quest IV (I love this game, I love how it tries to give you a mini story in each city you find, it's really a great and addicting RPG. If you love RPGs you CAN'T go wrong with this game. You will spend 40 hours easily, or more)
3°-Final Fantasy IV
4°-Shin Megami Tensei: Devil Survivor
5°-Nostalgia
6°-Luminous Arc (it's similar to Final Fantasy Tactics)
2D platform:
1°-Castlevania: Dawn Of Sorrow (it doesn't matter if you don't like Castlevania games, this game can make you change your mind)
2°-Henry Hatsworth in the Puzzling Adventure (this is a hard 2D platforming game where you can learn new moves such as double jump, climb walls etc. You can also upgrade your character and this game is a mix of puzzle and 2D platform)
3°-Kirby Super Star Ultra (I know... it's a remake, but just try to make 100% in this game and you will spend a big time playing it. To tell you the truth I never played the original on the snes, but this remake is a lot of fun.)
Point and Click/Adventure games:
1°-Time Hollow (I prefer the PW series but I think you like animes, so the storyline in this game and the art style will be better for you)
2°-Phoenix Wright (I strongly recommend you to start playing this series, and you should start with the first game.)
3°-Hotel Dusk
4°-Professor Layton
Other games:
1°-Rhythm Heaven (addicting and hard rhythm game)
2°-Geometry Wars: Galaxies
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