These notes apply to Acrobat X Pro. I don’t know about other versions or how to do this with free software. Adobe software is out of my price range too. I used my employer’s copy.
Good instructions for creating the fill-in are here.
Adobe provides instructions for making the fill-in saveable here, but it’s not clear the in their step 3 you want to pick File->Save As->Reader Extended PDF->Enable Additional Features…, not Enable Adding Text In Documents. That’s all it takes.