Inexpensive (as in lower $ cost) and "cheap" fabric are not always synonymous.
Unfortunately, experience is the best teacher for learning what one considers to be "good" fabric.
Incidentally - one of the most expensive cottons I ever purchased was a very finely woven, almost "see-through" batiste that I purchased for a baptismal gown/dress for my babies.
Also, I think the word "quality" should always have a modifier with it. Almost everything made has "quality" - good, bad, or indifferent.