Depends on how you intend to shut the thing down. If you use one that has an interface to the OS, it only needs to power it for long enough to shut the thing down. If you're going to have to power it until you respond to the beeping, much bigger.
Me, I'd use the battery for the PC only, and just plug the monitor into the surge side. The monitor doesn't need battery backup and that's 95% of the power in the cab.