I'm loving this topic, I'm also much interested to hear what other people say.
With that my answers:
When I look for comics I usually see the homepage "what's hot" etc. and from there see what's in the "recommended comics" at the bottom of episodes. But mostly I see around the forums for recommended comics
First I look at the comic to see if I like it's style, (layout, variety, eye-catching, pleasing to the eye, etc). Then, I'll start reading it. If I'm not in the mood I'll often scroll to a random page and if I like it I will flip back to the beginning and start to read it. If the story's catchy then I'll stick with it.
Genre: romance/action/adventure/ (things set in a fantasy realm/ introducing other cultures/ and sweeping landscapes and backgrounds )
Genre's I don't like: Mystery and super hero stories, also stories where people have special power elements or such (unless the comic is more focused on the character development and the culture of their world than just beating up the bad guy), Over-stereotyped things: anime girl or boy in highschool trying to fit in with all those cliche reactions and mentalities (Look up Anohana for an anime that helps break these stereotypes really well) , Super powerful-block head man who must save his world from an evil villan and get the girl, many stereotypical manga types (tsundere, b-baka!, getting overly embarassed or emotional over things that are so minute), fantasy in terms of elves, warewolves, vampires, etc (again unless it's different from the norm or big star movies (Lord of the Rings, Starwars, Twilight, etc)), Character who has a super special hidden talent which ulitmately makes them the superior savior that saves their world or something. Gag-a day comics (i like a longer complicated plot than just comedy jokes).
Genere i don't mind as long as it's good- Fantasy/action/adventure. Either focus heavily on the culture to make the world really come alive, or focus on the characters development (or both)
What makes a comic bad or good- If it can create a connection to the viewer, create a world that is tangible according to it's own universal laws, good art that's pleasing to the eye, good dialogue which matches the characters and can be read as a dialogue. That is good.
What makes me stop reading- If I no longer understand what's going on in the story, if the same plot is being re-hashed over and over again ("I'm sorry, your princess is in another castle"). [examples: CLAMP's tsubasa and xxxholic and almost Chobits (but it was close enough to the end that it didn't stop me from finishing it). At some point I just have no idea what's going on and wish things would just return to what it was like at the beginning of the comic. Bleach is a good example of constant re-hashing, Inuyasha too. (Inuyasha must save the damsel in distress again! Bleach: constant new characters with bigger and bigger boobies and swords with ridiculous powers! Wait, what, why are they all fighting in the sky again?). Comics with characters who are air heads or who are so random and so emotional you will stop reading the comic just because of that one character.
Lastly My comic- Hacheeachkee- I recommend it to those who like longer-complicated plots. It doesn't try to follow any stereotypes (infact it takes place on various planets with new species and cultures and worlds, nothing in the nature of common folklore like vampires and etc). There is no epic (have to save the world- i'm their only hope) plot, and focuses a lot more on relationships and adventuring and learning of new cultures.