Join the party; I just graduated and started my first job about a year ago. It's fun to make money. :-) I agree with the others--spend a few months throwing everything you can at your debts and getting enough cash for an (economical) car/apartment.
The best thing about being where you are right now is that you don't have to 'downsize'--I think my biggest helper towards eventual FI is that I decided BEFORE I finished school that I was perfectly happy living 'like a graduate student' forever, as long as I don't have to work forever. Keeping my graduate student furniture, basic cell phone, driving a toyota and shopping at goodwill were habits I consciously decided not to change. Thinking about your desired lifestyle right now--as you are--is great. I 'hide' my money from myself--in my case, we get 26 paychecks a year and my allowance is to spend one a month on all of my needs/wants--which almost exactly matches my previous once-a-month graduate student stipend in amount and frequency. The rest I quickly shunt away--first to my loans, now to retirement savings. With your costs being even lower right now thanks to your family, you have an even better opportunity for a few months. Use i! Even if you don't want to live quite at graduate-student level forever, it might be a great idea to do it for a couple of years to knock out as much as you can.
In your case, I think you can pretty easily knock out all of your debts pretty fast and get yourself sorted, possibly by around the time your fiance graduates. In the meantime, you two should start talking about priorities. I agree that not saving for retirement is a bad idea--I would probably start making at least the company match as soon as you pay off your own debts. Are there any options for your fiance to work in a way that would allow for partial payback on her loans? Such things are often options for teachers/doctors, and maybe for her too. Otherwise, are there ways for her and/or you to do side jobs in addition to your jobs? Maybe in addition to her day job she could have an evening/weekend practice on her own? I agree that you two, if you optimize apartment/job/etc well, can probably not only throw her entire salary at loans, but also put part of your salary into retirement savings AND have extra of your salary to put towards loans, too. And have a great life on top of that!
If the two of you together are grossing something near $140K you should manage to throw quite a bit at her debt yearly, save for retirement, and still have a decent (MMM-style) life. While in school making ~20K I still gave myself a $100/mo allowance for travel which was equal to several flights a year to see family as well as to amazing places--Dominican Republic, Costa Rica, etc--as long as I shopped around and was willing to travel on a shoestring, which happens to be my favorite way to travel anyway. I've actually cut my other costs since then, so I've generously increased my vacation allowance to $200/month now, which (for me) is so much that my allowed time off from work is more of a constraint than my travel budget. I think you'll be pleasantly surprised when the paychecks start rolling in, as long as you throw them towards things that are important to you (getting out of debt, retirement, and things that matter) and not consumer-things that don't. It goes a long way!
Have fun!