i've been reading
cucumber quest but it's not like actual heavily story-driven or anything but i like it
i also read
dominic deegan which starts off kinda goofy but gets p serious later on (also the art gets better lol) [edit: i just went and checked and apparently it ended like a year ago, so it won't get updated any more]
i linked to the first pages of both cos idk if the main page might be spoilers or not so w/ever
i'm not very good at judging what's a "good story-driven" thingimajig but those two are the only webcomics that come to mind
i'm not sure if its okay if i also mention
tgchan which has a /quest/ board that is basically just like webcomics where you can suggest stuff
iirc i can't actually post links to forums or discussion boards or anything like that? i'm not really sure...