The filters I use often are: CP filter, ND 2 & 4 stop filters, and 2&4-stop graduated density filters for controlling bright sky, dark ground. The last I don't use often, but there are shots that you just can't make well without them.
If you invest in glass, then putting cheap glass or plastic in front of the lens just doesn't make sense. I've learned the hard way when a bunch of shots were ruined because I used a cheap UV filter... Didn't notice until I got home and uploaded the shots - some were sharp as expected, but others were kinda blurred. Once I figured out what was going on, I got rid of the cheap filter and replaced it with a much more expensive filter... and tested it to make sure there was no image deterioration with it on. That was my take-away lesson, when you add to your gear, test it first before using it in a shooting situation.
As for whether UV filter works for you - test it. Take some shots under identical conditions with the filter on and off. If there is no difference, you don't need it for UV. Of course, you need to be at a location/scene where UV "may" be a factor.