The World Ends With You, get that first if you could find it.
Here's what you should do.
Buy a DS
Buy TWEWY
Buy extra styli. Preferably, the ones with extension or pen like.
If you have the collect-em-all syndrome, this game will last you a very very long time.
Next up, Dragon Quest Monster: Joker.
Once you're done with those 2 titles, you should be familiar with what DS has to offer and you'll know what other games to buy.