Having a puppy AND a baby in the apartment could most certainly be a little hectic. I think adopting an older dog would be fabulous! Especially if you are interested in protection, because it would take a few months (or maybe even a year) for a puppy to be ready to protect your home. Older dogs are not necessarily "problem" dogs. If you are going the route of adopting, older dogs can lose their home for a variety of reasons that usually have nothing to do with the behavior. For example: the death of an owner, new home restrictions, allergies, new baby, loss of job, a move, change in work schedule, etc. Many older dogs usually (though there is a chance that it won't be) come trained and may even have mastered basic commands like sit or stay. Not to mention the saying "you can't teach an old dog new tricks" is practically false. Digs can be trained at any age and older dogs are just as smart as younger ones. They also have a larger attention span than puppies, which makes them easier to train.
I would love to hear about your experience if you do adopt an older dog! I am currently a junior in college with plans to go to grad school after graduation. I am thinking about rescuing an older dog to have a companion while being in a new town. Dogs really are a (wo)man's best friend, plus they always make me feel safe & protected.