I strongly advise that you wash all the fabrics before cutting them - so you know how they will behave when they get dunked.
I'm also in favor of washing battings like warm n natural before using them, too.
But that's because I prefer the flatter look to a finished quilt.
As far as the diagonal stitching - if one has a zigzag machine - set it for a very narrow zigzag when doing the diagonal stitching. That will allow some give to the quilting.
If you have extra fabric left over, a matching or coordinating pillowcase might be fun.