Need help sewing playmat for baby

Hello I'm new here and a novice at sewing anything.  I would like to sew a 6 ft x 6 ft playmat for my baby who is learning to crawl (we only have wood floors).  All of the playmats I can buy have two problems, too small, and not sufficient padding for wood floors.  So I decided I want to make one for my little one.  I want the padding to be so thick that if he were to face plant, he won't get hurt.  I would like it to be machine washable so that the inside material doesn't clump or gather.  So how would I go about doing this?  What type of materials would I need and how much?  Also how would I sew the whole thing together?  Any and all help is greatly appreciated!

UPDATE: Ok so I was thinking what if I sewed the outside pattern fabric with a waterproof backing sewed 3 sides and put a zipper on the 4th and filled with foam padding.  That way any messes won't penetrate the foam and I can remove the foam cover for washing?  Would this work?

Also I would need to know if sewing this by hand what types of stitches would be best for sewing the waterproof backing onto the "design" fabric and sewing the edges.