Check the HM Revenue and Customs website (www.hmrc.gov.uk). Basically, gifts have to be less than £36 (linky), so you're SOL there.
To do things above board, you will pay VAT (17.5% of the value of the goods plus shipping costs - that's £175 per £1000). You may also pay import duty - I'm not sure whether a desktop PC is exempt or not (I know laptops are).
IME the additional charges tend to wipe out the savings. If you think you can still save, you might want to check out www.myus.com or www.shopthestates.com -- both give you a US shipping address that allows you to buy stuff from US etailers and they then ship it on to you. MyUS claims that they're able to (legally) list a low value on the shipping manifest, thereby saving you some VAT and duty (disclaimer -- I've never used these services, I just know they exist).
As for moving to the US, it's fun for a while, but most people I know move back to the UK/Ireland/Europe in the end (I was in Boston for a year followed by 4 years in San Francisco). You have to bear in mind things like the lack of an NHS, and the existence of 5 bazillion utterly **** TV and radio channels. And most importantly, you can't get proper bacon anywhere .