You can, and should, start whenever you want to. I would recommend not starting right your first week though, because at this point you really don't know how tough or easy your coursework is going to be. But after you take a few exams, and start to get the hang of things, if you feel like you have a couple hours a week to spare, then you can go ahead and get involved in something. Obviously if you're struggling in your classes, then you should just focus on that. I also wouldn't worry about reference letters at this point. Go to office hours if you need help with the material, not because you want to become friends with the prof (although the prof knowing you is never a bad thing). As far as volunteering goes, you can volunteer at a hospital, but I really don't know how worthwhile it is. Maybe its hospital dependent, but the people who volunteer at our hospitals don't really regard it as a great experience. I would look to maybe volunteer at some sort of free clinic or nursing home, or somewhere else that isn't saturated with volunteers already. And some general advice: your gpa should be the most important priority for you at this point. Make sure to get off to as best a start as possible, as it may be nice to have a little cushion when you get to some of those upper-level classes. And at the end of the day, gpa, along with mcat (which you shouldn't be worried about right now), are the most important factors that med schools will consider. But even looking beyond just med schools, if you have a strong gpa, it will help you no matter what field you ultimately decide to enter.
Good luck, and make sure to enjoy this summer off!
