I've never done it, but THIS site looks good. In short, use diamond hole saw with water for lube in a slightly oversized sealed guide hole to keep drill steady but slightly cocked so only one part of hole saw grinds on glass at a time until complete circle has been made.

@chas045 For glass I would definitely go that route. For a plastic that drills out easily, I really want to find a larger bit in the same style as the one I found. It may not exist though.

Diamond hole saw, lubricated with water, in a drill press, with a very gentle touch.

For plastic, use a drill designed for plastic. For smaller holes there are twist drills with a much more acute point than wood or metal drills (like a 30 deg angle), for larger holes in plastic forstner bits work fine.

Diamond hole saw as mentioned by rweigand, but for holes that large I may opt for cutting oil instead of water.

I did buy a kit of diamond hole saws, but these were a gigantic pain. When I tried to start the cut into the plastic, the bit wanders everywhere. I would have to fashion a polyethylene shell to hold everything in place, which is a bigger investment in tooling than I want. I ended up having to cut a 3/4 inch hole into the plastic with a wood drill bit, which risked destroying/cracking the plastic. That created an uneven hole. I then had to go into that with the diamond hole saw to even out the hole. I will now have to go at that hole with a filing kit to get the burrs of plastic out of the hole.

The bit I photographed in the original post cut through my plastic like a knife through butter, and a 3/4" bit of that type would have worked much better than what I am struggling with now.

Yeah, that is definitely not for plastic/acrylic. Ad rweigand states, a forstner bit would be the way to go.

@rwiegand Okay, I will try to buy some Forstner serrated bits

So I ended up with a collection of Forstner bits, and these seem to work pretty well for plastic. The attached photo shows how I got a fairly clean cut using a hand drill.