I had preemie twins, born at 34 weeks. One of my girls was on oxygen for 7 weeks, mainly because we live at 6,000 ft. The thing to remember is that preemies are just like other babies and have the same needs - only more-so. With ours, you have to feed more often because their little bellies can't hold very much and weight gain is extremely important. The hospital might give you a supplement to add to their formula. We had 22 cal. Ask about that.
The other issue we had was with respiratory problems. You might make sure that the baby is okay in that capacity and really watch out for respiratory infections. Their little lungs aren't as well developed as full term babies, so you have to be very careful about exposing them to illnesses. Avoid places like Wal-Mart, the airport and places where germs like to hang out. When preemies get sick, it can be life-threatening.
Right now it's summer and the risk of that type of infecion isn't as severe, but watch out in the fall. Ask your doctor about getting the baby the Synagis shot - which is to prevent RSV. RSV is very serious and potentially life-threatening in all babies, but esp preemies. A home health nurse will come to your house to give it and if you don't have insurance, it's really expensive.
Most importantly, don't be afraid of "breaking" your preemie because she or he is smaller. They are just like all babies and need plenty of love and human contact. We held our babies all the time and I think it's really important to their developmment. There've been studies done that show that infant massage on preemies helps them thrive - gain weight, leave the hospital sooner, etc.
Good luck and congratulations!