do not wash the blocks / tops before quilting-binding
you can machine quilt them if that's what you want to do- if you plan on keeping these quilts for family not expecting them to be in shows/museums- it is a personal choice how you finish them -- muslin was used often for quilt backs- there are many different weights/qualities of muslin choose a good one.
enjoy your new treasures- don't sweat the small stuff. after quilting & binding wash very gently in cold water- if there's a lot of color you may want to toss in a couple color catchers or use synthropol in the water.