Start off with Final Fantasy IV for your Square-Enix game. It will have a classic style and very well done storyline. From there, I'd suggest moving onto either Square's The World Ends With You or Atlus' Shin Megami Tensei: Devil Survivor.
Regarding the Mario and Luigi RPGs, just go ahead and grab Partners in Time. If you like it, then begin anticipating Bowser's Inside Story. I thought the game was pretty fun and charming, but I would personally recommend a half dozen other RPGs on the DS before M&L, including the three I recommended to you in the last paragraph.
Go ahead and grab the first game in the Ace Attorney series to start yourself off with. I've personally never played them, but plenty of others vouch for them. Still, start with one game at a time in case it's not for you. In the same vein, get Hotel Dusk: Room 215. It's my favorite point and click adventure title on the DS, and has one of my favorite stories this gen.
Now for some random suggestions, I'll give you a few favorites of mine other than those I previously mentioned:
Advance Wars: Dual Strike
Castlevania: Dawn of Sorrow
Peggle DS
Brain Age
100 Classic Books Collection
Personal Trainer: Cooking
MLB Power Pros 2009
Guitar Hero DS
Yoshi's Island DS
Bangai-O Spirits
Retro Game Challenge
Space Invaders Extreme
Trauma Center: Under the Knife 2
Mystery Dungeon: Shiren the Wanderer
Moon
Dementium: The Ward
Bleach: Dark Souls
Metroid Prime Pinball
Contra 4
Metal Slug 7
Little Red Riding Hood's Zombie BBQ
Chronos Twin
Elite Beat Agents
Anno 1701
Knights in the Nightmare
Disgaea
Valkyrie Profile: Covenant of the Plume
Ask me about any if you have questions.
Tag: Became a freaking mod and a complete douche, coincidentally, at the same time.
