How fresh the coffee you are using is just as important as the overall quality of the coffee. Coffee that is freshly roasted and stored properly produces a superior cup.
Ideally you should start with a good quality coffee, such as Arabica or other premium blends, that is as fresh as possible. It should be noted that freshness doesn't necessarily correlate with when the coffee was actually roasted. For instance, a coffee that was roasted six months ago but was vacuum-packed in a can with minimal residual oxygen would be fresher than a coffee roasted a month ago but left open to the elements.