Apply for the maximum amount you would like to borrow and plan for the unexpected. You can always pay your loan back early with no prepayment penalties.
Some expenses to consider are the costs associated with moving including a moving truck, boxes, movers, security deposits often 2-3 months of rent, utility deposits, and incidental expenses.
Consider the timing of your first paycheck. Your first payment may be due on your loan before you receive your paycheck.