Get a shelter mutt. My dog is a shelter mutt and he is the most awesome and loyal dog ever. I live in an apartment, too and know many others who live in them. Avoid getting a large dog. Many apartments have a weight limit on dogs, and for good reason. They tend to make a lot of noise from romping around and the neighbors below complain, and large dogs need a hell of a lot of exercise that is not compatible with apartment life. I personally find small dogs highly annoying, so I got a medium sized lab mix at the shelter. His name is Aries. I'd say for minimal grooming also get a dog with short or medium length fur, but my dog has long fur and I only need to brush him out a couple times a year.
Thank you everyone for all of your input so far. I just talked to my BF about possibly adopting a Greyhound- there's a dog track near here that adopts out retired racers- and he wasn't opposed to it. They also apparently allow you to use their track for running your sighthounds.
Just to clarify, I'm looking for a dog with at least above-average energy levels, because I'm planning to have them as a workout partner as well as a watchdog. I don't want a dog that is overly sensitive or will continue to bark long after the 'threat' is gone, just one that will let us know when someone's at the door or something doesn't seem 'right' to them.
Depending on what region you're living in, you might want to consider getting a cur. They're more common among hunters in the Appalacians and the South. Curs are good guard dogs, very territorial, but they can be taught to be very calm and social when away from "home."
They're short-haired dogs. The black-mouth yellow curs often get mistaken for yellow labs, so there would be little worry about the dog being stolen or anything like that.
The New Jersey wildlife department employs yellow curs to help run off nuisance bears from residential/public areas, so you know these dogs are tough. They're not intimidated easily by size or injuries.