The system requirements for most BFG games are fairly low - so I couldn't imagine you'd have any issues with a new PC (although, I would try to avoid anything with an Intel Graphics Processor).
Even though Windows Home Premium doesn't support XP Mode it will run Virtual PC (including Windows Virtual PC).
Compatibility under Windows 7 is pretty good, much better than Vista. It's probably not going to be a problem unless you enjoy retro gaming. For those games I use emulation (DOSBox, VPC or VMware).
What price range are you interested in? If you have a specific model you're interested in, post it - we'll look it up for you.