Lens flare caused by a UV filter on a lens can be an issue in very rare circumstances. Rare enough, that in a 1/2 century of photography I can't remember encountering one of these instances. I also can't recall ever having scratched a front lens element since I always keep them protected with UV filters.
Admittedly, it's a little difficult to judge since the contrast reduction due to flare can be quite subtle, but my advice is to protect the lens with a UV filter and leave it there unless you need another filter. It isn't likely to cause you an adverse contrast problem. If it does, your post production should be able to correct it.
I'm a big believer in lens hoods. Not only do they also protect the lens but they really cut down flare - way more than a filter can enhance it. The only problem with using large filters with step down rings is that you may have a hard time finding appropriate lens hoods for wide angle lenses and zooms. But, basically, the advice above is sound. Just note that one issue. I'm lucky in that all my lenses use 77mm filter except for the macro lens which has 62mm threads.
Since you're shooting digital, it is hard to imagine the need for any filter beyond a UV protector and a polarizer - possibly a ND filter if you need to use a slow shutter speed in bright available light. Everything else can be applied to the image in post production.