Shoul I get a 3" hole bit or just take an exacto-knife and go around and around a few hundred times?
If you do this, you will scratch your plexi repeatedly, as you can't possibly be perfect with each cut.
Someone here once posted about using a homemade jig for this, which I believe involved using a strip of wood (a paint-can stirrer, I believe) with a nail at one end and the other mounted to a hole-saw arbor on the other, 1.5 inches away. The arbor drilled into the center of the hole while the nail cut the circumference.
On a side note... If you had to choose a pc pinball game to use on your cabinet, which would you use?
Visual Pinball with Visual PinMAME. Most FE's support it these days.