As a rule, I'm always on the look-out for new comics. I enjoy seeing what different people can do with the medium, and I like the wide expression of ideas. Of course, there's always limitations I have to set for myself. Back when I was a kid working as a caddy part-time at a golf course with extremely limited income, I simply couldn't afford too wide a range of comics. As I grew older, time became a more limiting factor. Not that I could afford to buy everything that looked good, naturally, but I could afford to buy more than I had time to read.
These days, I still have limitations to contend with. Money is still a factor, of course, and I've been having to limit myself to free online comics. But time is still a factor, as well, and I've fallen woefully behind on several of the longer-form web comics that I've enjoyed. (Mostly the ones where I came to the story pretty late in the first place, and had a great deal of catching up to do.)
But I still try to pick up new strips as I find them. Especially ones that are written so that a new reader can jump in to the middle of it quickly, or those which are new enough that there's not much catching up to do in the first place.
I try to give each comic a fair shot. Any one episode (whether that's one strip a day, or six pages once a week, or whatever) doesn't really convey a good sense of the creator's ability, I feel. It might be a good (or bad) episode in and of itself, but it could be just a bit of a fluke the episode turned out the way it did. Maybe the creator's normally really funny, but just happened to have an off day when I started reading. Or maybe the creator normally sucks and just happened to come up with a brief piece of brilliance by accident. In either case, I try to read a comic for a little while to get a feel for it overall before deciding to continue with it or not.
Generally, I don't have a set time limit that I'll give to a comic during their trial period. Just however long it takes for me to get a good feel for it.
But I have noticed a trend. I have a tendency to give more leeway to artists who employ an illustration style I like.
For example, I've been reading Day by Day by Chris Muir for a few weeks now. But I don't particularly care for it; I just don't find it very engaging. I'm even impressed that, despite having a generally conservative viewpoint that I disagree with, Muir maintains a relatively intelligent and substantive perspective. But I just find that the strips fall flat for me. But I've continued reading as long as I have because I like his illustrative style.
On the other end of the spectrum, we have the widely popular xkcd. I find that the strip falls just as flat for me as Day by Day; I see and understand the jokes -- I just find them terribly unfunny. I've tried on several separate occasions to read it, but I can't get through more than a couple strips because the art is so bad. Even for stick figures, they're poorly done in my opinion.
Both strips are equally unengaging for me, but I've given Day by Day (who's political views often directly contradict mine) more tolerance than xkcd (who's thoughts and opinions are more in line with my own). Now, that's not to say I won't read a poorly drawn comic, just that I set the bar much higher when it comes to a comic's writing if it's drawn poorly.
I'm certain it's not a bias that everyone shares, but it's a point worth recognizing in myself. Knowing that I'm not keen on bad art and tend to dismiss it more readily, I know I should make an extra effort to appreciate poorly illustrated comics on the chance that I'm dismissing something special for superficial reasons.
That said, I still don't like Achewood.