I was using 2-1/2" coarse Kreg pocket hole screws. Kreg screws are supposed to be self-tapping, but the coarse-thread screws are intended to be self-tapping in softwood, and the fine-thread screws they intend for use in hardwoods aren't available in 2-1/2" lengths. I decided to drill pilot holes in the oak. Just to make sure, I did a test hole in the scrap piece I'd cut off.
Flip the base upright, put the MDF on top of it, then use a straightedge to draw two straight lines joining the outside edges of the legs and extending the width of the MDF. I used the countertop as the straightedge. We cut it with our cutting guide, which is based on the factory edge of a sheet of 1/4" plywood, so it should be straight enough. Use a carpenter's square to transfer these lines onto the ends of the MDF.
If you're using drywall screws, you'll want to countersink the holes. Drywall screws are flat-head, and need a countersink to seat solidly. If you're using Kreg pocket screws, the way I did, you won't want to counter-sink the holes. Kreg screws are pan-head, and seat just fine against a flat surface. Both drywall screws and Kreg pocket screws are self-threading, so you don't need pilot holes in the second sheet of MDF.

Grizzly is a company currently undergoing an upheaval. This brand was once known as a manufacturer of professional grade tools and equipment for woodworking products. Though, in recent years, that reputation has begun to slip a bit since being bought by the Chinese company SIEG. These days, whether the Grizzly product stands up to its previous standards of excellence often has more to do with what you are buying than the company itself.