In a manner of speaking the home you purchased has a "UPS" of its own.
I started out on my venture into the world of living off grid striving to spend as little money as possible. This demeanor payed off then but after years of living off grid with that same equipment; batteries, inverters, electrical, I would suggest to someone else starting out on this same venture "don't scrimp." If at all possible go ahead and get the 20 year batteries, the best true sine wave inverters, the latest charge controller technology, all new electrical ie; wire, disconects, conduits, etc., etc..
Its alomst time for me to replace my battery bank and the price's have nearly doubled. The inverter has lost some off its capability and has been responsible for the demise of a monitor and a tv and a dust buster amoung other things. You have to be careful with a modidied sine wave or modified square wave (they are the same thing) inveter. The device may seem to operate fine for a while but in time can destroy it and there is no way to know what will and what will not survive being powered by such an inverter.
Writing to you from an e machines computor and monitor (2nd monitor) powered by a Trace DR-1512 that has lost its ability too switch over automaticaly from one vac. input to another and charge batteries.
As for your computors UPS, you may not need it if your home has a system monitor such as the Bogart Tri-Metric, you will learn what times, if any, to not use the computor for fear power loss from weak batteries. That would depend on how well the PV system was designed as compared to how it is uesd. One of the functions of the inverter, is a low battery voltage disconect. Which is something your UPS has as well.