Like CoachBob I've made thousands of foam popper bodies.
I use the puncehs from Harbor Freight. I didn't get the ones with the nice 1/4 inch drill insert in them, so I had a friend machine them down to fit my 1/2 inch drill press. The largest size, the one that makes 1/2 inch 'blanks' is plenty big for bass/pike/inshore saltwater stuff.
I turn mine on the dremel with the needle set up CoachBob showed us all several (many?) years ago. I have 'altered' mine to include a base plate with small pins to insure against 'spinning' on the mandrel.
There are places online that sell drill mounted punches and mandrels designed for this application. You can get the plugcutters in larger diameters there. They are not expensive, if you plan to make a bunch of poppers, but I haven't bought them simply because the method I use works just fine and I have little need for larger diameter foam baits. Once I get past 1/2 inch, I go to balsa bodies turned on a wood lathe. Primarily because they are lighter.
Something CoachBob didn't mention is cutting the popper body flat on the bottom. I just take a razor blade and slice it after it's been glued in place, the smooth with a sanding drum in a dremel. I do this with almost all of my baits larger than 3/8 inch diameter. Clears the hook gape a bit which aids in hooking percentages. You don't have to use as long a shank hook then.
Buddy
It Just Doesn't Matter....