Lots of questions, most answers will only be opinion, so here is what I would do:
Motherboard DP35DP
Processor Q6600
8GB RAM speed is not that important, so go for a cheap, middle option
PSU can often be the noisiest component. Do a little research and be prepared to spend another £20, if necessary.
XP64 (if you can still get it).
Cat 5e cross-over cable, or Cat 5e cable connected to a managed switch, if you want to add more PCs to the network at some stage.
Use Remote Desktop to connect your two computers.
The above will cost around £400-£450. If you run out of RAM, build another PC and add it to your network.
As soon as you start talking about more than 8GB RAM in one machine, the cost rockets.
DG