I started reading comics again in college. There was a comic book shop next to the used record place I went to.
I started off reading Marvel, especially X-Men and Wolverine. I have the original '82 series and most of the v2 run. I gave up on Marvel when the x-men split up into many factions and there were about 15 series running concurrently. I also collected spiderman for a while, when Todd Macfarlane was drawing it. Good stuff.
I got into Batman years before, when the Dark Knight Returns came out. that's what got me into reading comics in the first place. I'm a huge fan of the elseworlds series, which puts Batman in different periods of history. They've lost me in the last few years, with the whole 'death of Batman' thing. I still read the non-canon one-shot stuff, it's very gritty and always interesting.
My current recommendations:
Y: the last man
BONE, by Jeff Smith
Sandman and associated comics
The Watchmen, and pretty much anything by Alan Moore
The Maxx, by Sam Kieth
Sin City, by Frank Miller
Kick Ass (I)
The Stand (Comic book adaptation of Stephen King's novel)
Anything Hellboy or BPRD
House of Mystery (a distant tie-in to Sandman)
Kick Ass (II)
If you liked the long Halloween (I have the original comics of those. amazing artwork), you need to read Catwoman: When in Rome and Batman: Dark Victory. Both of those series continue the story where Long Halloween left off.