I am pretty sure that the ones who do a credit check are mainly concerned about your credit score, your criminal background, and whether you have a steady job that will pay the bills. I think whether you have a broad credit background is less important than if your score is high or low, and 700's is a good credit score. If you are employed and can give them your job reference to confirm that you can pay the bills, you should be OK.
If you are a student, they will probably ask you to have a parent or guardian with a full time job co-sign. When I was a student, they would never believe me when I explained that student aid provides students with living expenses money, they always said if you don't have a full time job they need a cosigner who does.
