I have a DS, and I've loved it since I got it. I probably would have liked a PSP just as much, but DS was more within my price range at the time and I liked the 'innovation' better. But that's my opinion.
Please, for the love of all that is good, buy a system for the games, not brand loyalty. I'm pretty sure you're not going to go 'zomg nieeeeeentendo/P14Y574510n for da wiiien' But it's a general comment.
Yes, the DS can play other things than games, but you need specific hardware that comes separately, isn't Nintendo endorsed and costs as much as the DS it's self, or more, in most cases. Not worth the hassle, again in my opinion.
Anyway, in summary; Go with whatever you want. If you really want something that plays videos and music however, try an Ipod or similar, because they're purpose built for that sort of thing.