Tools to make a uniform cut and the polishing are two different worries
Personally I'd mark both my intended line of cut and a second line a couple mm above it, Place tape over both lines (or place the tape first if the lines wont show through it) and then use a dremel or rotozip to cut on the top line - doesnt matter if I wander a little on that part. Then I'd take a sander and smooth it down to the first line, in the process erasing any gross irregularities from the cut. Then I go to my stock of wet&dry sandpaper and sand the edge wet at 200 grit until I cant see the marks of the coarser sander. Then 400, 800 and 1600, each to remove the marks of the last. Keep going with finer and finer grit until you give up and put some buffing compound on a wheel in that dremel and finish it off that way.
If I can put a mirror finish on steel that way, I can probably polish a cut edge of plexiglass smooth