First, have you exhausted any federal student loans available to you? As well as any grants/scholarships you might qualify or apply for? If not, do that first. Federal loans have a lot more protections and options for delaying payment if you hit a rough patch, as well as forgiveness options for certain professions.
Next, I would try to grab something with a fixed rate if you can. Unless you plan to pay these loans off fairly quickly, expect the Prime Rate to go up over the life of the loan. it can't go much lower after all. As far as the amount you borrow, I think you can opt to have your financial aid office return any overpayment to the lender (thereby reducing the amount you borrow) rather than taking the difference as a check. At least this is the case with federal loans. So you should be able to borrow the right amount either way you go.
Past that, go with an institution that you like to work with. A lot of folks have Sallie Mae horror stories. They took over one of my federal loans and I've had a couple mishaps with their auto-pay system that would have caused a late payment if I didn't watch the account like a hawk. But that experience isn't universal.
