No games, and just regular DVD playback, you won't see a difference between these cards. Get the cheaper one.
If you ever plan to playback HD-DVDs or Blu-Ray disks in the future though, the 8600 GT is definitely the way to go. It has HD video image quality enhancement features the 8300 GS won't be able to match.
I think it's worth mentioning that if you're going to go with an 8300 series card you should seriously be considering one that is passively cooled. Even the 8600 can be found in a passively cooled version... you've made it clear you're not a gamer, but everyone loves silence right?