In terms of retirement planning at this stage you should be putting money in in this order (to kind of simply what they're saying above):
1) Hospital 401k/403b up to their match amount (ex. if they match 50% up to 5% of your income, contribute that whole 5% since you're essentially getting 50% guaranteed return for free) which will be taken out pre-tax
2) Roth IRA up to max $5500/yr (most IRAs will let you auto-withdraw monthly out of a savings/checking account if you want to spread it out over the year)
3) If you can afford it after you max out your Roth IRA, have them take more out for your 401k/403b (ex. increase from the 5% above to 10%).
Remember that a 401k/403b is different from an IRA in that you can't just put money in whenever you want. Your employer has to take a set amount out of your paycheck every month, so if you want to contribute more you need to have them take out a little more with each paycheck. On the other hand, with an IRA you can dump $5500 in once any time during the year, spread it out into monthly contributions or anything in between.
Your employer may not offer a Roth option of the 401k/403b, but if they do it's advantageous for you to contribute to that instead of the traditional 401k/403b since your earnings will compound over the next 20+ years tax free (you pay taxes up front but nothing down the line). In a pinch, you can also withdraw your contributions from a Roth IRA or retirement account early if you really need to since you've already paid taxes on them (this would obviously be a last resort). In contrast, your tax savings at this point are pretty minimal from contributing to a traditional 401k compared to how much you'll save in taxes down the line on a Roth 401k/403b.