I don't have a Shopbot, but run projects on a CNC Shark, Probotix Meteor, and a Multicam 3000.
I have a personal Shark and a newer one I supervise where I work. My Shark runs from a 4 year old Dell running Vista. Of course it offloads the cut file to an SD card in the controller, so doesn't have to be speedy to keep up. Running VCarve on that machine is a bit sluggish but it only bothers me when I try and render a complicated tool path. The work Shark runs from a newer (one year old now) PC with an i5 rpocessor and 512 gigs. We also run VCarve and Rhino and most of AutoCAD's suite on it with no problem. Again, these machines offload their g-code to the controller.
The Multicam has run for two years now, and the PC it started with was 2-years old demoted from a PC lab. It has been upgraded this year, but never been challenged in feeding files to the CNC. Where the newer PC shows up better is in running whatever CAD application or CAM for rendering.
My Meteor came with a quad-core PC, 256gb ram, and runs LinuxCNC only. It has to feed the controller over parallel and doesn't get bothered with other tasks while a job is cutting.
Laptops/notebooks often have hardware power saving features that can interrupt a CNC job in progress. You can use one, but be sure and turn off all screen saver/power saver options. You may need to go into hardware settings to make sure it doesn't power down the USB ports.
I scanned ShopbotTools.com for PC recommendations, and didn't find anything. Email their support or give them a call and I'll bet you get an answer quick.