I'm not a battery expert, but I have quite a bit of practical experience repairing UPSs. Battery failures are a very common problem, but battery fires are not. The most common failure mode for a lead acid battery is it just stops working. Sometimes some acid leaks out. Compared to lithium based batteries, they are very safe.

If you do buy a UPS, get one with a good warranty from a reputable supplier. In my (biased) experience, it's quite common for the internal electronics to fail. The repairs are usually pretty straight forward, but it's easier under warranty :)