I agree with paying down the loans. But If you are chafing at the bit to get started, I don't think there's any harm in setting up a Roth IRA for yourself, funding it with a small amount, and setting up automatic contributions of a small amount per month. This will get you started learning the ropes. By a small amount, I mean such a small amount that it doesn't really interfere much with paying down those loans, paying the electric bill, saving up for a car so that someday you can buy one without financing it, etc. Be careful, though, that you set it up in such a way that you're not incurring any nasty regular account maintenance fees.
Just to be specific--this is not a recommendation, and there are lots of ways to set it up, but just for instance. You could start a Roth IRA at Vanguard. You could make a $1,000 purchase of the Vanguard Target Retirement 2045 fund. You should sign up for electronic delivery of statements so that you won't get dinged $20 a year for account maintenance fees. You could arrange to have further automatic purchases of $50 a month made out of your checking account. (If you don't want to invest that much, you'd have to talk to Vanguard--the minimum seems to be $50 but I think the interval could be longer than once a month).
You'll get your hands dirty with the paperwork, the terminology, see what the annual form 5498 looks like, learn your way around the Vanguard website, have something to talk about in this forum. You'll get to see just how much a stock fund's balance goes up and down--when you hear that "the market plunged" by golly you can log into your account and see how your retirement savings plunged--and find out how you feel about that.
If your wife wants to set one up too, fine. That should be her independent decision.
Only do this if you want to. Keep the amounts low enough not to matter a whole lot. Then a few years from now when you want to get more serious about it, you'll have a better idea what your options are and what questions you need to think about.
For 401(k) versus Roth IRA, I seriously doubt that one is hugely better or worse than the other, except that if your 401(k) plan has an employer match you want to get that. The usual reason for having both is that you've maxed out one of them and are looking for another tax-advantaged place to save more.
Personally, I never have been able to save except through automatic deduction--and the best way I was able to get my savings rate up was to wait for a raise and then bump up the deduction a bit, so that I was putting some of the raise away but still taking more home.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.