Battery life on the PSP depends on the game you are playing and/or if you're watching a movie. I'm told the battery life could be better for watching movies (only around 2 hrs +/-) but that varies. Additionally, there are many external devices that can extend battery life, and some have external speakers like this one:
http://www.etoys.com/genProduct.html/PID/4523139/ctid/19?cpncode=07-1203687-2&srccode=cii_13389012
As for the music issue, the PSP will play MP3's but it doesn't use an internal HD like an Ipod. It uses Sony-style memory sticks (more expensive than SD memory cards for the equivalent memory) which come in a variety of sizes from 8MB to 2GB (2 gig runs you about $145!) You can convert movie files from DVD's to a format you can save to a memory card and watch on your PSP, or you can buy movies in the UMD format (though it's more expensive than a DVD and has fewer features.)
I was debating between the PSP and a Dell Axim pocket PC, the purchase price was roughly the same. The thing that made me choose the Pocket PC was that it was much cheaper to do the things I wanted to do with it (ie. watch movies, play cheap/free games, occasionally use the wireless internet, read books, etc.) Both the PSP and Pocket PC allow you to do these things, but it's cheaper on the PPC.
If you're a hard-core gamer who doesn't mind dropping $40-50 for a new game, the PSP is awesome. If you're looking for a multi-media device that will let you listen to music, watch movies, and maybe play some games, check out the Pocket PC options on Dell.com, or Ebay. Good luck.