Lucifer is fantastic, as is Astro City and Grant Morrison’s The Invisibles. (Although that last one is very tough and it takes two reads at least to appreciate it.)
Next time you’re in a Borders, find their “Graphic Novel” section, which will have many trade paperback reprints of various series (including several mentioned above.) Go ahead and read through a few issues of anything that looks interesting.
Also, don’t discount superheroes – most of the superhero books published these days aren’t your typical slugfests, or at least not always. Read the first couple issues of Batgirl (there’s a trade of this, too) to see what I mean.
Finally, I’d also recommend the CrosssGen compendia. These are big thick books that collect ~8 issues of a handful of comics series published by CrossGen, and they’re cheap. The first one, Forge #1, is probably your best bet and just came out a few weeks ago. All the series reprinted in Forge will continue in the next issue of Forge, so you’ll be able to follow the entire story.
As for websites, I’d recommend CrossGen’s at www.crossgen.com or the message boards at the DC Comics site.