First off - get an external hard drive from LaCie if your computer is otherwise fine...or maybe a laptop, which would let you be more mobile.
You probably don't need a new computer if you've just used up all of your hard drive - if it's running slow, it'll probably need more RAM.
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If this was a few years ago, I would have said "Dell", but now I would say "Don't bother"
If it's a new PC you're looking for...maybe try getting a HD Jobbie from a Sony Centre...
As long as you get a PC which costs upwards of £800 you should be fine. Pay proper prices and you'll get a proper PC - pay any less than £800 to a company - PC World especially - and you're gonna get ripped off.