Loans from workplace retirement plans can be risky because the entire sum will become due immediately if you leave your job; if you fail to repay it, any remainder counts as an early distribution subject to income tax and the 10% early withdrawal penalty.
That said, if you think needing to access this money is relatively unlikely, your better bet is probably to max out the retirement account, take a loan from it if you really need to, and work on establishing a suitable emergency fund outside your 403(b) within a couple of years.