Pick up a decent gaming machine. The rest will fall into line.
Gaming is probably one of the most power-intensive applications. If you get a machine that can run modern high-graphic games, it'll run almost anything else.
A laptop is nice nowadays. Works as a desk machine, but you can still take it places. Get Windows 7, 64 bit. The gaming engines still offer it.
Start here. The designs are a bit twee, but they work and it's a well-known brand. Note that the base model is probably all you need, and it's about half your target price.
I would upgrade Windows 7 Home to Premium or Ultimate, but that's not essential.