Don't know whether I'm classified as "picky" or not, but here's my method. 100% cotton; Dresses, blouse and men's shirts; large sizes (more fabric); fewest battern pieces (less fabric waste; and prints and stripes; Children clothing (only with licensed characters that can be used to set a theme.
Some thrift shops have plastic bags of sewing/quilting scraps. I look for bags with 100% cotton; large scraps, and interesting prints. I stay away from bags with poly, satin, or other fabics rarely used in quilts.
Am I "picky".
One more thing, I always visit these places before I hit Walmart, JoAnn, Hancock, etc. I could quilt the rest of my life and never use the stash I have, but I keep buying. Being 70 years old and the mother of 4 sons, I've made it clear that #3 inherits contents of quilt room. Since I've been disabled, he drives me all over and he'l learned so much about fabric that I even trust him to go get "fat Quarters", colored batiks, 30s repos, Civil War repos, etc. He helps me spray baste my quilt sandwiches, etc. but he draws the line at siting down at the machine LOL. I haven't given up hope though. Each of my sons have their own special place in my life and heart, but every mother should have one of these.