No point going for the monster pc right now, get something a little below top spec, as the spec comes down a little the price drops a lot. Top of the range computer equipment is always very expensive.
Im sure you can get a dual core pc easily with that budget.
I wouldnt buy anything less than a dual core tho.
Im currently saving to get my pc upgraded, should have a new motherboard+quad core cpu, memory, video card by this time next month. Its costing me £374 for the parts.
Not entirely cheap for the parts, but the parts are pretty good spec.
You should try going to a pc engineer that can build a pc for you, it is by far the cheapest and most readily upgradable option. Failing that, do a little research and build your own, and save even more money.