At home, I have had a single rack w/ network and server gear for more than a decade and I always run two good quality UPS, that I run a test on annually, tied to two different circuits. My setup now is a bit annoying because I'm renting currently, but when I owned a home prior to my recent move I had an electrician run two 20A Dual Function (AFCI+GFCI) circuits with hospital grade outlets to power the two UPSes in the same room but on separate circuits and breakers at the panel. I don't think that's overkill, but I think anything more would be overkill at home. When I buy a house again, I intend to do the same.
Since buying better quality UPS and testing them regularly so I can replace batteries when needed I haven't had any fires, but using batteries past their useful lifespan can greatly increase risk of fire. Expect that you should replace the batteries every 3-5 years, and that they will cost nearly as much as the UPS itself. If you're not comfortable with that, invest in a quality surge protector instead and figure out how to deal with failures. UPS batteries are a big fire risk, so you need to understand it and work to contain it. Also, keep a good dry fire extinguisher near your rackmount equipment and get it tested annually.