You can use one monitor with 2 computers.
You can either unplug the monitor each time you want to change between them, or buy a video switch so you can flick a switch to change the monitor between computers.
For gaming, the CPU doesn't have much of an impact.
If you have a large budget like that, I'd go with an Intel Core 2 Duo, because it is much more powerful than an AMD processor, and therefore you will benefit form the increased performance when you're not gaming. Plus it will help slightly when you are gaming.
Hope this helps.