Although I don't have a DS, or any other handheld for that matter, my two best friends do, and they both say its brilliant. Also, if you can get to a Wi-Fi hotspot, you can play online, and if its a wi-fi hotspot such as MacDonalds or an internet cafe, then you can go online for free.
In the event that you do go ahead and purchase one, may I recommend Animal Crossing: Wild World? Both of my mates play this every day, and they're in their early 20s! Also, the New Super Mario Bros is meant to be good.
The PSP has far superior graphics and power; but nowhere near the selection of games. Plus, its a lot more expensive.