I've purchased and washed the Waverly cotton fabrics from Walmart and have been happy with them. I do overcast the raw edges before machine washing.
I did not notice any pilling, the shrinkage was in line with the LQS fabric shrinkage (I measured before and after), and a couple of the dark ones had some excess dye, but none of them were bleeders.
I do think it is a bit on the coarsely woven side - but I also think some of the LQS fabrics are also on the coarsely woven side.