show, you can get them for around $50.

A UPS has a limited time it will run (especially a $50 one). That limits
its usefulness.

For long power outages, you will run out of juice and your tank will start
experiencing problems.

For short outages, it won't make any real differences.

For medium length outages it will. But these I believe are the least
likely. By this I mean your more likely to have a 0-5 minute outage (not
problem to tank) or many hours to days (your UPS goes dead long before it is
over). You should be able to request from your power company (or find on
their web site) the duration's of there outages to verify this.

A generator will be able to last as long as you have gas.
If you don't want to buy a generator, but use the UPS you setup, I would
recommend you plug in as little as possible. A heater and small pump, most
likely.