Although you do want a high tooth count for a higher-quality cut, an ultra-high tooth count can be detrimental. With a 100T 7-1/4" blade, you'll have to cut more slowly and may burn the plastic.
If using a 7-1/4" circular saw blade, use a high-quality 50-60 tooth blade, which will perform similarly to the 10" 80T blade that Aloysius Defenestrate's local plastics company recommended.
To help protect against chipout at the edges, you can either tape the cut line or you can sandwich your Plexiglas between two thin pieces of sacrificial plywood or MDF.
Assuming your plastic is, indeed, Plexiglas (acrylic), you can polish the edges with a torch. Do NOT use a torch on the edges of Lexan (polycarbonate), because you'll just melt it. If you aren't sure which type of plastic you have, acrylic is bright when you look directly at the edge, while polycarbonate is dark when you look directly at the edge.