Is a desktop pc or a laptop better for me to record gameplay?

I have around £600–630 from christmas and I want to buy a HD PVR to record my Xbox 360 gameplay..I have a HD television (720p its works on for my xbox) and i know this laptop isnt that good/fast at the moment so i want to buy a laptop for it to work but then my friend told me a PC would work better.
So after the PVR £150–180 I would have around £450 left to buy a laptop or desktop pc, if you can could you please share some links with PC’s are in that price range and will work with the PVR, thanks.