Many, many years ago I took a community education class on plastic fabrication techniques...heat forming, cutting, welding, finishing, etc.. What I remember re easiest cutting was a sharp carbide-tipped blade for the 10" table saw having a minimum of 80 teeth, the more the better. Reason: You want to take small, clean, shaving-type bites, rather than chunky 'mouthfuls' more common with soft wood. This, plus a slow steady feed will give you a very clean chip-free edge.
However, anymore I use the advice above and go to our local plastics fabrication company here in Flint, MI, SOROC Plastics. They're excellent, accommodating, and reasonably priced. When we built our store layouts, we had them cut the sliding/fixed clear panels for the periphery. We also asked them to put a 'flamed' edge on the panels. Flaming is a technique of some skill in which a butane flame is passed along the cut edge of the plastic to quickly melt the surface and corners of the edge to give a smooth, clear, polished appearance. VERY professional-looking. It's not something you want to do yourself without serious practice. At SOROC, it was a SOP that cost a few dollars total for the panels we ordered...WELL worth it.
Another thought about the panels. We didn't use plexi-glass (a.k.a., Lexan) because of its expense. We chose 1/8" acrylic...much less costly. Reason? Sure, in a barrier situation it will need regular cleaning of dust, fingerprints, ...boogers!..., and everything else that the viewing world can throw at it. As such it will, as sure as God made green apples, get scratched and lose its clarity. Plexiglass is tough to survive rough handling, blows, bullets, etc., but it, too, will scratch. Polishing out the scratches is not a time-effective alternative. Rather, we decided that the lower cost of acrylic would justify eventually re-purchasing replacement panels when the optical clarity was unacceptable. AND acrylic is SO much easier to work with. You just have to understand that it can't take excessive bending stress that the plexi's might survive.
Just some thoughts for sharing...
KD