If I were to get a dog, I would be looking at an Alaskan Klee Kai or a Shiba Inu. Alaskan Klee Kais are like miniature Huskies that stay small. The Shiba Inu from what I heard can live in apartments since they're known to be quiet, medium sized, and independent. However I'd feel bad leaving it in the apartment from 8 am to 5 pm everyday... Plus I've had dogs before and know how much attention they need. I agree dental school may not be the best time for a dog.
I never had a cat before so I know little to nothing about them. Since everyone here loves cats, how about a Munchkin? I could watch it scurry around the room while doing my waxing. Σ:3
Chances are I might wait it out a little before getting a pet. It might be wise to see how the workload is first since the first two years are very time consuming. I'll post a picture if I do though.