Build Advice Custom Build Gaming PC Specs

Hi guys,
This is my first post on this forum . I have recently realised that my Dell Dimension 8300 is not actually very good for any new games that come out. It even struggles playing old games, and I usually have to play on the lowest graphical settings. I NEED A NEW PC!

All I want to use it for is gaming, and maybe surfing the web, coursework etc. I have talked to my dad about buying a pre-built gaming PC off internet buying services (Ebay etc.) and he said it would be cheaper and I'd get a better PC if we built one. He referred me to here and other forums to ask for advice on specs. So here I am.

Right, let's get started:
Budget:£350
HD: I need a big HD for games. I would prefer 300GB+
Graphics Card: ATI Radeon if possible. Good enough to play games on medium-high setting.
Processor: Dual/Quad Core, (Whatever you guys recommend) 2.5Ghz+
Memory: Whatever you guys think is best
Operating System: Windows 7.
Others parts are open to recommendation

Many Thanks,

Will