Definetly have guests sign squares to be assembled later, and not a finished quilt.
You do not want to risk that someone would do something stupid and ruin a quilt. (For example- most of the people I know who put cameras on tables either got a ton of pictures taken by children of their food, or a few "rude" pictures taken by drunk adults- I don't think anyone would TRY to ruin the quilt, but you just never know...)
Have 25-50% more squares than you think you need. People will feel pressure to sign perfectly, children might need more than one try.
Put up a sign that says to sign in the center of the square, unless you want to pre-piece squares to make only the center signable (to deal with the seam allowance issue).
I'd have a variety of pen colors, so people can be more individualized.
I've always gotten my muslin at fabric.com, but don't know if it is the quality you are looking for.
This is such an amazing idea!