Cartoonists (and artists in general, I suppose) love to argue. Or, at least, we have strong opinions on things; spend all your free time cloistered and toiling, you're bound to ruminate. One favored topic is the ol' “Art vs. Writing” debate, which usually seems to degenerate into “I think I'm good at X, and know that I'm terrible at Y, but that's okay, because isn't X more important, anyway?"
Truth is, if your goal is to make quality comics, Art and Writing are equally important. Intertwined. Yin and Yang. If one falls short, the other suffers. Which can be discouraging, because people tend to think that they're gifted with certain talents and not others, and thus it shall ever be. But Art and Writing are skills, not talents, and like all skills, you can improve your proficiency over time.
Nearly every artist, barring the rare prodigy, starts off by producing horrible art. Most just have the good sense not to to show it to anyone, which isn't an indulgence that most webcartoonists enjoy. Your immediate goal is to just start drawing. Produce! Make bad comics. Then make the next batch a little better. Always draw a bit outside of your comfort zone; if the thought of drawing hands intimidates you, then you'd better draw a whole lotta hands. Once you feel like you've mastered rendering your characters from a certain angle, switch it up for a panel and draw them from behind or use a bird's-eye view. Don't get comfortable.
If you feel inclined to ape another cartoonist's style when you're starting out, that's fine; we all learn through imitation. But ultimately, you've got to experiment and figure out what works for you. Study the works of artists in different media. Watch some early animation, check out a museum; you may not like everything you see, but perhaps you'll notice a certain effect or learn a technique that you'll want to incorporate into your own work.
And finally, don't obsess over tools and materials. When you're just starting out, you don't need a Cintiq or a Moleskine or a collection of Copic markers. And you don't need the full Adobe Creative Suite, when Photoshop Elements will do. You may find that you want these things later on, once you have the skills to utilize them to their fullest potential, but when you're making horrible art, you'll want to do it as cheaply and conveniently as possible.
As your art skills improve, you may find that it has an effect on your writing. Instead of thinking, “I'd better write the script like this, because I can only draw these things,” you'll gradually switch to “Well, this is the script I came up with, so I guess this is what I'm gonna have to draw.” Eventually, you'll get comfortable enough to let your art stand on its own when necessary; sometimes, the best-written scenes have no words at all.