Marine batteries are one possible choice. Another option is golf cart batteries, but since they're usually 6 volts instead of 12, you'd need two of them. Look for "sealed" or "maintenence-free" batteries, as regular lead-acid batteries will give off explosive hydrogen fumes. Just to be safe, don't put the batteries in an enclosed area like a drawer or closet where hydrogen can build up.
Further notes for using a homebuilt UPS: When you're running your computer off battery power, turn it off before the battery reaches a 50% discharge level. Marine and golf cart batteries are more resistant than car batteries to damage from being discharged too far, but they're still expensive to replace.