It really depends on how important your documents are.
You don’t want to be in the middle of some grand architectural drawing or a literary masterpiece when the power goes off. If your only surfing the web and gaming etc then a UPS is not so important.
There is also the possibility that your operating system could become corrupted with an unexpected shutdown but this can usually be remedied by doing a rollback.

(ps you wouldn’t need the surge protector if you had a UPS as they have one built in)

I’ve actually never heard of a battery backup for a desktop PC

One major factor that this depends on is how often your area has power failures.

We rarely get them in the Los Angeles area.

A computer at where I used to work had a UPS (“Uninterruptible” Power Supply) that went bad and I lost about 2 hours of writing that I had done.
This happened because the UPS was in line with the power cord, and when the UPS went bad, power to the PC was lost before I had a chance to save what I had written, even though there was no loss of power to the electrical outlet itself.

If you have one or more power failures per year in your area, then a UPS can be worthwhile, but if those power failures are less frequent, then a UPS is more of a potential vulnerability.

@Rarebear : Here’s an example of a UPS (backup battery for desktop PCs and other electronics).

Like @Odysseus says, a UPS has a built-in surge protector, so you don’t need both.

I live in an area that loses power occasionally, so it makes sense for me to have one. It also makes sense if you live someplace with “brownouts” like where I used to live in the woods.

@Brian1946 Many people seem to think that the batteries last forever and never even check to make sure they are still working.

Mine has come to my rescue a number of times. But that definitely depends on how often your power goes out. In your case, I would suggest getting one.

When we bought our most recent desktop, we bought a UPS that also serves as lightning protection. I think most all of them have this feature.My house has been hit twice so i’m a little sensitive and over protective though.
We were told that UPS’s also “smooth” the little spikes too. Don’t know if it was sales hype, but we bought one.

@alamo They do, in fact, smooth out the power. Having a steady input voltage going into the computer’s power supply is a good thing. “Steady” here being a smooth sine wave of consistent amplitude, as wall outlets provide AC power.