Try these. There’s cheaper options, but this style may work better for you. Two step process of drilling hole and then countersinking, but you’re not going to break it.
Amana Tool 55227 Carbide Tipped 82 Degree Countersink Set with Adjustable Drill Bit Depth Stop and No-Thrust Ball Bearing 3/8 Dia x 1/8 Drill Dia x 1/4 Inch Quick Release Hex Shank