You didn't say how thick it was...
but for all but the thinnest of lexan, I've used a table saw with a fine tooth carbide blade. (these are sometimes called a 'plywood blade') A jigsaw will work, but your chances of cracking the material are a lot greater and it's pretty hard to hold a straight line. Also, if you do use a table saw, you'll likely have some melting of the material at the cut, so either go real slow or cut wide by about 1/8" and then sand to final dimension. For the rounded corners, I'd probably use a table sander or just mount a sanding disk in the table saw (basically the same thing) and finish them by hand. A table router would also do the trick. You don't really need to tape the cut to prevent chipping, but its easier to draw your lines on the tape and then start cutting.Hope that helps,Jeff