You should get Zelda PH. It isn't as big as the console games, but it is still a lot of fun and the stylus controls work great. Haven't played Hotel Dusk though, so I don't know about that one.

Other games you should get:

Mario & Luigi: Partners in Time
Kirby Canvas Curse
Mario Kart DS
Chrono Trigger (when it comes out)

Get FFIV, I'm planning on getting it next week after I'm done with III...

congatz on getting a DS! Other poeple have already said the ones I would recommend.

It really is a great time to be a DS owner. TTEWY recently released, as did FFIV. A new Castlevania is around the bend, as it Chrono Trigger, Dragonquest, Disgaea, GTA, all kinds of crap.

My essentials are:

Phoenix Wright: Ace Attorney
The World Ends With You
Hotel Dusk
Phantom Hourglass
Mario Kart DS
Elite Beat Agents
Final Fantasy IV
Castlevania Dawn of Sorrow
NSMB

Those games will let you dip you feet into what the DS is all about. There are even more games coming out just this year, that look to top many of those games. Chrono Trigger DS, new Castlevania with world map, Disgaea.

Next year we get the Suda game, Fire Emblem DS(I hope), and like a thousand JRPGs, lol.

Some games I feel remiss not to mention are: Advance Wars, Ninja Gaiden DS, and Professor Layton. Then there's always FFTA2 and Rings of Fate. The former very well reviewed. If you liked FFXII, you should get Reverant Wings. Then there's Picross, and Contra, also about a million other puzzle/action games that I can't remember, lol.