Poster, use double sided tape and stick it on the vinyl window, not the wall. Then, use a warm iron over the plastic (make sure it’s the thick kind, not the cheap kind) to smooth out creases. It may take practice.
Getting Federal tax credits this time of year is a good idea, because you can get the rebate pretty soon after you’ve spent the money (as opposed to doing something in January and waiting a year). Just make sure it’s a refundable credit- I have no idea.