There are different quality fabrics. It depends on what I am making as to how fussy I am with the quality of the fabric. If I am making something more disposable or trendy like quilted pot holders, microwave bowl holders, tissue holders, mug rugs etc. then lesser quality fabric is OK with me because of the time I will have invested in it and the length of time I expect it to be used. If I am making a full sized quilt however that will take a lot of time and effort to construct it and it will have a longer life then I will use higher quality fabric.
I go a lot by the feel of the fabric - called "the hand" in quilting lingo. It will feel more fluid, less cardboardy and you will not be able to see through it. The majority of the fabric at a quilt shop or a few fabric shops will be this type of fabric. In addition to that the people that generally work at these stores sew and know their products and are are interested in what you are making. The quality of fabric runs the gamut at the big chain stores (such as JoAnn's, Walmart, Hobby Lobby) and you have to be careful what you are getting. I have also found that often the person cutting the fabric in these stores does not sew and really can't offer any advice or enthusiasm on your project.
Buying fabric on-line is another experience since you can't feel the fabric or get a really good idea of the true colors. In this instance I go by past experience and others recommendations. I have bought fabric on-line for projects or when I see something on sale that I am willing to take a risk on. Here brand names can also help you decide on what the potential quality of the fabric will be or past experience like on a site like Connecting Threads where they only carry their own fabric.
It is a skill that is developed over time and you will win some and lose some.