Short form: Trust your own senses and feel and whether a fabric is worth your time to deal with. You will develop preferences, but it is a reason many of us don't want to buy on-line, we are each looking for certain things. Price/name brand can help but are not guarantees.
There are many ways to judge fabric quality, one of which is thread count, however dye saturation/treatments like metallic embellishments also add to cost/quality. The term for the raw fabric is "greige" goods and many things can be done to the exact same piece of raw woven cotton and different industrial rolls of fabric can be woven differently. Among things I'm looking at is how the fabric drapes, that bias movement and I don't think most quilters even look at that. But mostly you want a nice straight and even weave that you can't see through, you shouldn't feel the individual threads, it shouldn't ravel.
Ultimately we have to be the judges of what fabrics we use, I have gotten some very high quality pieces of fabric from Walmart (I think some of the Wamsutta pieces are from high-end products and not exactly made for selling as yardage) and I've gotten brand names from the LQS (Local Quilt Store) that after I prewashed I considered non-usable. We have many discussions here on prewashing, all I can say is I'm a fan and I believe my projects are better for taking the time to do it.
Some of what is sold at Joann, Walmart, etc. is considered "craft" quality, which is a general division and is perfectly fine for things like seasonal table cloths or clothing that is not meant to be forever. It is typically mixed in with the other fabrics or may be in it's own (often seasonal) group. You can often see as well as feel the difference and for those of us sensitive to smells, there may be some distinct odors of starch or other treatments. Often the designs are not very complex, nor is the printing very close, and the colors "cheap" from the lack of saturation.
Quilting quality may be slightly different than LQS quality (usually meaning the name brands like Moda, Benartex, etc.), but has a higher thread count and typically then a tighter weave (less see through). Many people associate a certain weight of fabric as a sign of quality, however other people (including me) just love working with batiks or lawn fabrics because they are also (typically) quality fabric just of a different weave.
A lot of people believe in pure cotton for quilting, I can say that I prefer it for enough reasons to be a thread of its own (like prewashing), but I haven't always had the luxury or the right color or whatever it is on why I wish to add in a blend of some sort. Sometimes it is for texture, a bit of linen or silk or whatever again in fabric that is prewashed is not a concern to me and I've worked with a 10% spandax fabric because it was perfect for the person. And I have a huge horrible piece of slippery poly blend that's probably somewhere around the 40/60 (mostly poly) that I'm going to use for the back of a quilt just because I love it and its perfect for that project but it will be a pain to work with and it may or may not last -- just never know with the polys some of the most surprising flimsy fabrics turn out to survive direct nuclear blasts and others just disappear.