As you'll be an intern there, I'm pretty sure you won't have to ask to get the exposure you're looking for. In getting medical experience it's often what you make of it. I volunteered in a free clinic, and some (like me) worked solely with the patients while others just hung out in the pharmacy room and counted pills. It seemed like they were just putting in the time so they could put it on their application.
If they give you the option, I'd just ask to see as many different cases as you can and try to get as much patient interaction as you can. Personally, I've helped dig out things from people's ears and observed external hemorrhoid surgery.
You should have the opportunity to see and experience a lot.
As for what schools look for, at least as far as I experienced, is that you see different aspects of the occupation. I picked out three or four individual experiences that really stuck out for me, and that's what I talked about during my interviews.
Good luck, and enjoy the experience.
