If you're looking for a Superman story, look no further than All-Star Superman by Grant Morrison and Frank Quietly. While it's a wee bit dense in parts and really utilizes all aspects of Superman's mythology (even parts some would rather forget), I have never read a more perfect Superman story and in many ways, I don't think I ever need to read another Superman story (but I will break that in September when he starts on Action Comics!).
I'm going to have to second Y: The Last Man. It's one of the few series' where I bought many trades at a time (I bought 2, 3, 4 and 5 at once). Man, when I discovered it, I raced through it. It's also the only series I've read that could work in any medium without adaption and not lose anything. Comic, Novel Series, Film, Radio Serial, Television, Rock Opera (maybe not that last one). Just an amazing well written series. As far as adult content, there's the occasional tame sex scene, female and male (in only one case as far as I know) nudity, some light violence and some cartoon gore (the art really isn't that realistic)
Also, are there any characters you're especially interested in. I am fond of the statement that there're no bad characters, just bad stories (and the converse). So each character has amazing stories and stories that define them. So if you let us know who you're interested in and perhaps what kinds of stories you're interested in, we can better direct you to comics you'd enjoy.
Last statement: I'm not sure if anyone told you here, but DC Comics is "relaunching" in September. With everything restarting at #1, some with some type of rebooted continuity. So if you want to start with regular monthlies (the bread and butter of the comic industry for the past 70 years), that will be a great place to start and they're designing it so you wouldn't have had to read a single comic before that point.
Cool! Thanks for the info.
And I've been counting down the days until September 1st since they first announced The New 52. At this point I'm planning on working through some of the older stuff until September, and then probably doing a combo of older and newer stuff.
As for characters I'm most interested in:
Pretty much any members of the Batman, and Superman Families
Green Lantern (all of them)
Zatanna (They don't have any of her stuff on Comixology, but I might be willing to pick up some trades of her stuff)
Legion of Superheroes (same deal as Zatanna)