Yes, open a savings account paying at least 1% (online: Ally, CIT, or Synchrony) to store your emergency fund. You should have a minimum of $1,000, & then save 3-6 months of your fixed expenses. A credit card backup is good but not a substitute for your emergency fund. Even if your checking account is paying 1% (most don't), having your emergency fund in another account & bank makes it less tempting. Link the two for transfers.
I agree with setting your 401K initially for the employer match & fully funding your HSA. Assuming your 401K is the traditional kind, both will lower your Adjusted Gross Income for federal income tax. Once you have your emergency fund, max out your 401K to the full 18000 when you have a full year to work with. You can also fund a Roth IRA up to a max of $5,500/year for tax free earnings forever. Anything extra after this should go towards your loans, which effectively gives you a 5% return for your payment.
Consider including an International Stock Fund in your allocation mix.
Do not buy a new car or any other debt at this time.