The last point is where you'll see the biggest difference, between different filters and when comparing filtered/unfiltered. This old test took a large selection of the UV filters that were available at the time and shot with them in conditions where you'd expect to see flare:
https://www.lenstip.com/113.1-article-UV_filters_test.html
From the images, there are some pretty big differences (you can ignore the stuff about UV absorbance). Uncoated filters were pretty poor, and multicoated were better than single-coated. Today, I would choose filters with (a) multi-coating, (b) an 'easy clean' layer (multi-coated filters without this, like Hoya's old Pro-1 and Super HMC ranges, tend to smear when you clean them) and (c) high quality optical glass (which should be a given in the multi-coated ranges from Hoya or B+W). Hoya Fusion / Evo filters are quite reasonably priced. Their HD range are more expensive but tougher. B+W MRC and MRC-Nano are both excellent, and they come in brass mounts that are less likely to bind.