I prefer LQS, Amish shops or mennonite shops and shopping on line. On line I have never been disappointed in quality except once with some closeout stuff I got from Connecting Threads. I liked the thickness of the fab but the printing process they used on it was heavy, almost rubbery. But I only paid around $3 a yard. It will get used somewhere. I have been disappointed in that the color wasn't exactly what I thought it was on a few occasions. Again the fabric will eventually be used, just not for the project intended.
I have been burned by Jo Anne fabric so will not buy fabric there. It faded horribly and did not last and this is in i a quilt that doesn't get heavy use. I will buy notions and such from there and batting but not fabric.
When I spend years working on a hand quilted quilt I DO want it to last so I will buy the best I can afford and shy away from the big box stores like Walmart, Hobby Lobby and JoAnnes.
Batting is something else you should consider. If you are handquilting I would stay away from W&N or W&W. Very difficult to needle. If you want 100% cotton you can try Mountain Mist, Hobbs, or Quilters Dream but QD cotton batting is very very low loft. Your BAQ sounds like it should have wool batting! Dreamy to handquilt and heirloom quality.