I used 1/2 inch screws but 3/8 should work well. You should be able to get the screws at any hardware shop.
The screw covers come in two parts. The clear part goes under the screw head when you put the screw in just like a washer with raised part up around the screw head. The white cover snaps on after the screw is tight. Most RV dealers and parts companies can get the screw covers. I did this fifteen years ago and I can't remember where I got them. If you are not near an RV parts retailer, you can easily buy them on-line. Type "RV Screw Covers" into Google.
I included photos of the labels of the screws and covers in a previous post. The screw covers come in more than one size but you can see which I used in the photo.
Good luck with your project.