There is no precise halachic standard of absorbency for bedikah cloths; they just have to be white and of a natural material such as cotton. While you are correct in your observation that the pre-packaged clothes tend to be thin and not that absorbent, they are completely acceptable for use and in practice will show stains when they are present. Some women find it more comfortable to tear up well washed old white cotton underwear or undershirts, which tend to be softer as well as more absorbent. All bedikah cloths should be checked just prior to use to assure that there are no pre-existing stains or small red or black fibers which could lead to confusion.