Probably a good idea to try listening to a few different bits and pieces in your price range, to get a sense of what you like - £800 is a lot to spend on a recommendation

You could also try looking secondhand - you get more for your money (and, in the case of mission speakers, I find the older ones such as the 73x series tend to sound better than the new models I've heard...); also, if you later change your mind about what you like you should be able to sell on the stuff with less of a loss.
You should get a significantly better-sounding stereo setup if you just buy that (stereo amps tend to be better than AV for music, and obviously you'll have more money to spend per speaker) but obviously you won't get surround, and some DVDs don't sound as good in plain stereo... I've chose to spend my money on a stereo set-up, but then I use it more for music than DVDs. If you do go for stereo and your PC is your main source, you could also look at getting a stereo DAC (secondhand there's plenty of choice under £100) to run your PC through, which may improve quality.
Jon