I'm picky about fabric quality, but also keep the purpose in mind.
I am obsessive about squaring the fabric on the grain line before I cut. I see so many tutorials where they don't do this (Or maybe they just don't show it?) and it makes my teeth hurt.

Watson

I made a dress once where the head of a zebra was over my left boob and the butt was over my right boob. Didn't notice that until I wore the dress. Made the same mistake when I bought a tshirt that had a large dog on the front...you probably know just where the large eyes fell. I must be a slow learner.

For fabric that I'm going to wear, I want it to drape softly and not be thin. For quilting, I look for color first and the feel of the fabric second. I wil put up with things being off grain. I once bought a fabulous fabric that I just loved. It had scenes in squares...except the fabric was printed off grain a little bit. I just added a slender strip of fabric to one side to square it up and turned out fabulously!