Right had a quick look about and this is pretty much your options.
Intel i3 Build - Over budget, crap motherboard, ram/cpu/gfx/psu/case/hdd is all fine for what your needing it for, tho personally i wouldnt go too cheap on a case, i went for the Antec 300 case and its perfect, good space and good cooling once you add a few fans (Silent ones) made the mistake of adding my old coloured fans for a little extra air, sounded like a helicopter taking off.
AMD Build - Still over budget but not by much, better motherboard but loss a little on CPU power, wont really need much to run what you want anyway.
I currently run a E8400 @4Ghz / XFX 4890 1GB OC / 4GB DDR2 1200+ ram and it runs anything i throw at it.
Its very hard to fit a decent build into £350 unless you go the route i went, that system cost me less than £200 to build a year ago buying used/second hand parts and selling my old ones on from AV forums, with your £350 you could build yourself up a very nice little i3 system, i myself am considering selling on this build and starting fresh on an i5 possibly i7 build using the same method as before
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Good luck with your build hope this gives you a start to work on, personally i would either look into AV forum computer classifieds if you have time to wait on the build or throw a little more cash at it, get that i3 build with a better motherboard and it will run like a dream.
