No matter what you end up doing preparation of the driveway is of the utmost importance.
I'd recommend removing the grass and dirt with the use of a sodcutter. You'll literally have to cut the driveway down about 6" below the level you ultimately want it at.
Come back with some class 5 limestone for a base, usually costs about $150-250 per 10 yards. Class 5 works well as a paver base, or a base for concrete, and it should be down for at least one full year before you put the new driveway down.
The total cost of this project is about $250. It will look nice, doesn't track on the carpets, and will lead to the finished product of asphalt or concrete.