Honestly that's a tough question, I don't normally think about it.
Let's see... I like the silent, big, beefy, tough guy types who end up being softies with a pet or taking care of a small child. In the same vein I like the dangerous person who is now retired and doing normal shit, or turns into a grill dad or doting grandparent. (Like Tatsu from Gokushufudou: The Way of the House Husband)
Himbos and bimbos. Also valley girl and Californian surfer bros.
Angsty, sad, gothy, emo types that romanticize depression. Yeah, it's bad, but as someone whose been struggling with that garbage for ages those kind of characters are hilarious. Similarly I also like characters with anxiety for relatability reasons, and ones odd interests that most people wouldn't be into, like studying bugs or collecting bones. Maybe they're a hermit who hates people, but loves animals.
Not so much a single character, but a romantic couple that is super healthy, really into eachother, and can turn anything into foreplay. (Like Morticia and Gomez Addams)
Messed up, sort of anti-hero types. I love a protag who looks like a homeless druggy whose a total douche, that goes to whatever means to get what they want, but luckily wants what the audience does most of the time. There are a lot of characters like this but right now Nick Sax from Happy! and Randle McMurphy from One Flew Over the Cuckoo's Nest come to mind.
The character who plays dumb, but is actually really smart, and has been putting the pieces together the entire time behind the scenes. Or they somehow knew everything the whole time, and just waited till they get the smoking gun to show off. Imo Detective Benoit Blanc from Knives Out falls in this category, he seemed kinda incompetent at first, but pretty much knew everything from practically the beginning.
Unfortunately I don't have any deep reasons for liking characters, nor do I notice nuance enough to tell a complex character from a simple one... unless it's really obvious. I just like fiction. xP