I wouldn't use inferior (read cheap) plastic - it simply won't last. There are products like strataglass and lexan etc that do excellently duty as windows.
One other point: any plastic/acrylic/whatever you use that will stand up to the service will be tough to sew through, you'll need access to a heavy duty upholsterer's (or sailmaker's) type sewing machine - and the skills to use it.
1984 Fast/Nicholson 345 "FastForward"
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)