I disagree no pets, I always say cats are the best med student/resident companion ever
get 2 and large water/food dishes. yes it's ideal if you have more time for them, but seriously, they're fine if you only have an hour or two in the evening, or even have to be gone for a few days. as cruel as it sounds, even if I did a month long away rotation I would just have a friend 2x a week do the box and check food and water. they will live and come to forget this short period of loneliness. plenty of cats live outside with no creature comforts. mine were ecstatic when I came home & seemed none the worse for wear. they were also 2 shelter cats. all told, they live like princesses and like anyone have had a few hard times in their life.
as far as birds, I've had a cockatiel when I was equally busy. I don't know about a budgie.
if they are the type of creature that needs a friend in the cage, I think that's great. If you can get them from a shelter or otherwise rescue them, this will go a long way to easing your guilt over some of your long hours.
depending on the first two years' structure, you could choose to be home studying a lot. but keep in mind if you are the type that can do that. my bird was quiet so I easily could have had them out of the cage on a special perch right on my desk to "hang" with me to study, and little breaks to pet/play/treats. they never kept me up with noise when I put a sheet on the cage.
that sort of time home will be much more sporadic year 3. Year 4 is often as hard as you make it, which could be hard depending on what specialty you go for. After Oct you can set up a cush year with electives usually. As far as your school's 4th year requirements and how bad that is.... I dunno. You will have to be gone quite a few days for interviews, or even an away rotation
No matter your residency you're likely to hit 80 hours + /wk for the most part. There can be chill clinic or consult months or what have you somewhere in there... it will depend so much on specialty or program
Get them the biggest nicest tricked out cage you can afford. I don't know how they do with long hours to themselves, or with other humans besides their owner. See if there's other bird lovers in your school in your area and see if you can help each other out, often people end up on easy/hard rotations at different times.
Some types or individual animals do better/worse long stretches alone. The way I see it, if the bird has something "to do" or a friend in their cage, and they can tolerate just getting say an hour a day with you, it's fine. In nature, what would they be doing? Humans basically choose to live in cages (apts). I don't think many prey animals mind being in a sick tricked out condo, always a good temperature, always good food, clean water, a good mate, never any danger, provided they have something to do and someone to keep company. Just like with people, some days might be more or less boring than others. Some days might be sad days, other days you might have tons of time.
It depends on how budgies are.