I think it's fine to get a cat as a med student. Actually I recommend getting two because then they can interact with each other when you're not around.
I would suggest getting adult cats instead of kittens because adult cats will be less rowdy (usually) and "what you see is what you get" as far as energy level and personality. Plus adult cats have a harder time getting adopted at shelters so you will probably be saving their lives!
I adopted two adult cats when I was a 2nd year student and I still have them years later as a resident (I also ended up getting a dog during residency once I was sure I was able to handle the increased time demands of a dog, but dogs definitely require more time than cats).
I have had to move several times with the cats and it wasn't a big deal. They complained about being in the cat carriers but they were fine once they were in the new place.
🙂
Leaving cats alone for overnight call is not a problem as long as you put food and water out for them.
I bought gravity-based food and water bowls like this:
http://www.petsmart.com/product/index.jsp?productId=12474230 so it would be easy to leave them with plenty of food and water.
Honestly, you can even leave cats alone for several days in a row (again, just make sure you leave a lot of food and water out and clean the litterbox right before you leave). The cats seemed happy to see me when I came back the times that I did that, but I don't feel like it hurt them that I was gone. Cats are pretty independent animals and while some of them appreciate having people around, they don't need people in the way dogs seem to.