the trick to removing rivets is basically to grind down the flare/flange of the rivet so that the rivet drops out. You are not actually "drilling" out the rivet, just grinding off the "folded over" part that holds the rivet in place.
Use a drill bit exactly the same size as the flange
or ever so slightly smaller. As Nick said, the bit will follow the center hole of the rivet. You can also use a counter-sink type bit. The rivets are probably stainless so you may need to use an alloy bit.
Since you are replacing the pop-fit bezel with a screw-fit bezel, don't worry too much about messing up the part you are discarding. A really tight fit for the replacement screws is also not essential since you will be applying about a half inch wide seal of silicone glue/sealant around the base of the bezel.
I don't usually find myself not agreeing with Nick
but I would use the screws and nuts hat come with the portal kit. They are nylon and pretty much last forever. Ports I installed in '76 are still functional. Since they are not under real mechanical stress and you use a silicone glue/sealant they work fine. If you ever need to replace them - well, they will drill out very easily too. (You could also find that "stainless" does not necessarily mean "stainless". The market is flooded with sub-par grade "stainless" that does not hold up.)
Good project - have fun