first of all don't buy a laptop because you wont be able to get a good one for that price so desktop is your only option.
now if you want a good spec pc you can need to watch out for these components:
Processor: atleast a Core 2 with 2.6ghz. (not dual core they are different), Quad cores and
the new intel I series is good so go for the i5 if you can. AMD processors are very good for gaming to but they lack processing performance on video editing and other demanding programs
Ram (memory): atleast 2gb, (4gb is recommended)
hard drive: atleast 250gb
Video card: this is the most important component if you want a smooth playing experience so you should have atleast 512mb with 256bit rate DDR3 PCI-E (bit rate is very important because this is the processing speed of the videocard so dont go lower than 256bit. most video card on the market is only 128bit and that not enough).
power supply: atleast 450watts
now your easiest way is to buy a complete system and just replace the video card after, like i said most systems only have 128bit but choose the one with a good processor and a good RAM (memory).
where to buy? ebay is the cheapest but some sellers dont have after sales support so you need to ask before you buy, your safer with known shops like PC world, Currys etc but they will be a bit expensive. there are cpu only deals in ebay that have fantastic specs they have very reasonable price so you might to consider that but if you want to be on the safe side and you want to buy from the shops you should buy the ACER brand, ACER is one of the cheapest system with good specs and built quality on the market as far as i know. stay away from HP compaq, packard bell and sony. I would recommend DELL, dell computers are very reliable and durable and they use good components as well. they also do built your own system on their website so check them out too.
check out this links:
http://cgi.ebay.co.uk/Super-Fast-Gaming-Photo-Media-Workstation-PC-Core-i5-/400136240620?cmd=ViewItem&pt=UK_Computing_DesktopPCs&hash=item5d29fa7dec
http://cgi.ebay.co.uk/High-Spec-PC-QUAD-Intel-i7-920-6gb-DDR3-500GB-GT210-/400135991046?cmd=ViewItem&pt=UK_Computing_DesktopPCs&hash=item5d29f6af06
http://www1.euro.dell.com/uk/en/home/Desktops/inspiron-580/pd.aspx?refid=inspiron-580&s=dhs&cs=ukdhs1
http://www.pcworld.co.uk/gbuk/m3300-x6-gaming-pc-with-19-acer-led-backlit-monitor-06152791-pdt.html
you can see that the ones in ebay has far superior specs with a lower price than the one in the shop. so its up to you really.
hope this helps