Well, some of my favorites are comedy and some slice-of-life-stuff... but I could really get into comics of most genres as long as they're otherwise interesting? Character-driven is a big plus for me, as I'm very "character-focused" and often find the characters one of my favorite parts of an universe/story. A cool/interesting/appealing visual style is also a huge plus no matter what genre.
It would be easier to list what I'm NOT generally interested in(in comics or other media): the typical "european medieval" style high fantasy (that whole aesthetic just doesn't really appeal to me in general), romance, sports, stuff that's way to grimdark and serious. Though even some of these have some examples I still enjoy and could get into, so it's not always a complete dealbreaker if it's otherwise good (still don't think I'm gonna get into a super SRS BSNS grimdark comic though)
Yep, can definitely relate to this, the main reason I started reading Homestuck was Terezi - I kept seeing those weird grey people with horns around and thought "hmm this one with the red glasses seems really cool, I wanna know more about her"