Hi there, a few things you may need to consider)
1 )- battery life...if you have power available this means you can have a "better" spec as power isn't a limiting factor. An external mains(or car?) PSU is good value.
2)- temperature - can you keep the thing cool?
3) external HDD - you'll need to back-up valuable files (not just in case of theft).
4) Do you want to play video DVD's (this is when the processor power is tested), if you can avoid this, then the price will be a lot lower.
5) Firewire - for tape-based camcorders - try to avoid this requirement...it restricts your choice. Most cameras/camcorders use flash memory now.
6) Budget. sadly you only get low-spec small-screen PC's under £500 - you'll need nearer to £900 for something a bit better.
mp3 is a low-spec music file, so should be no problem, but a whole record collection can take up a lot of space. Replacing the PC HDD is likely to be expensive, so try to keep files elsewhere so the internal drive is reserved for the Operating System, programs, etc.
Video HD is processor sapping, so you need something like quad-core as a minimum, preferable more (like 6) with hyperthreading, which increases the throughput.
Not easy, is it?