I've used UPS's since I lived in the Arctic and won't live without them now. The 750Va rating of the PS is it's limit and it shouldn't be drawing that full time so a 750/800/1000 UPS should be sufficient.
In addition, I don't keep my monitor plugged in to the Backup side of the UPS either (hold-over from the days of CRT monitors) but it's all in easy reach (lesson learned) so if I have a blackout that looks like it will continue for more than a few secs and be worthy of a shutdown, I just unplug the monitor from the Protected side, plug into the battery backup side, do the shut down and return to normal.
LCD monitors draw less but are still a strain on the battery so best to at least power them down or do as above. No point in wasting batery power before you can get back and shut down the system. Also, think about the connected UPS systems with auto-shut-down software that senses the UPS coming online and does a proper close of programs and then the system if you tend to do critical work and have a flaky power company
Rob