DC, DC, and DC. Now, I'll admit, I've never read a lot of Marvel, a couple of Captain America and Black Panther comics that my brother leant me, but that's it. That said, I still strongly prefer DC.
DC has some incredibly deeply developed characters. If you've never read a Superman comic, you probably think he's a lot more flat than he actually is, but he's a really interesting character when the right writer gets his hands on him. And Wonder Woman is one of the most interesting characters around. Also, I really like Martian Manhunter, although unfortunately he doesn't have a running series right now, so he'll only be in JLA/JSA comics unless you get trade paperbacks, which, as Movie Bob said, are a really good way to get started. Ironically enough, considering that he's probably DC's most popular character right now, Batman actually isn't that interesting as a character, you make or break a Batman story based on the presentation of the villain, Batman is not the character most people actually show up for.
If I can suggest a couple of really good starting points (Trade Paperbacks in this case), or at the very least, places to break into the DC universe that'll really get you invested in what's going on:
Identity Crisis: Identity Crisis is a mystery story, the wife of The Elongated Man (one of the lesser known heroes of the DC universe) is murdered, and the investigation to find out who was behind the murder begins. Identity Crisis really gets to the core of the humanity of the heroes involved, and it would be just about impossible not to enjoy. I suggest it because it can be enjoyed on it's own even if you decide you don't want to pursue the DC universe, but it's also one hell of a great place to jump in.
Superman: Sacrifice/Wonder Woman: Mission's End: Both of these TPB's contain the issue in which Wonder Woman fights Superman, and while I would probably suggest Sacrifice over Mission's End they're both really good. Probably the most fascinating part of this particular story ark is that it really gets to the heart of the philosophies that drive the actions of both the heroes involved. It's one hell of a story, and if you read it, I can almost guarantee you'll want more.
Kingdom Come: My final suggestion is Kingdom Come, a series set in one hypothetical future of the DC universe in which the old guard of the DC universe (Supes, WW, Batman, Flash, Martian Manhunter, etc...) are aged, and end up in conflict with some of the newer up and coming heroes. Again, it's a pretty intense story, and it's really good. Also, since it's set in a hypothetical future, if you pick it up and don't like it, you won't really have to follow it up if you don't want to.
So, I would say give the DC universe a shot with any of these, if you don't like them, you'll still be free to pursue Marvel, though in my personal opinion I can't see why you'd want to... if you've ever seen an interview with Stan Lee, he falls somewhere between being a dick and a sellout, and while it's possible that the people who run DC are no different, I guess I feel like there's more integrity to the DC universe.
As an alternative option for you, there actually are some really good comics from independent publishers that you could give a shot to if you don't want to have to worry about continuity (I know I didn't when I first got into comics). Mike Mignola's Hellboy and BPRD (which was a sort of spin-off from Hellboy) series are incredibly good, they're published by Dark Horse. The art by itself justifies reading them, but if you like Lovecraftian themes then you absolutely can't go wrong with Hellboy. It may not offer the superhero stories you'd get from DC, but it's still really damn good. Also, The Walking Dead published, I believe, by Image Comics, is really good (it recently got a show I believe, though I haven't seen it). It's heavily character based, that is to say that the author derives the plot not from where he wants it to go, but from what he thinks the characters would do. If you've ever read a Stephen King story, it's a very similar writing process to that which King uses, and the result is some really deep well told characters. The benefit to this type of writing is that even if the plot wasn't good, it's still interesting to read because the characters are so enthralling. In this case though, you get the bonus of the fact that the plot is still really good. So I would also suggest The Walking Dead as a good comic series to read if you're interested in comics, but not sure if you're ready for the continuity yet.
