Not all cottons are created equal. Each textile ("type of fabric") has totally different properties. "Cotton" only describes the material that a particular fabric is made of, and is completely independent of whether it is knit or woven, or even the style of weave.
Not all woven fabrics are the same, either. A twill is completely different from a broadcloth, and both of those are different from sateen. Some are very stiff, some are thick, some are thin, and some are really drapey.
FYI, make sure you wash your fabric BEFORE you cut and sew anything. There are two reasons for this:
1) Fabric on the bolt is pre-treated with a chemical called "sizing". You need to wash that stuff out. Sizing often makes fabric stiffer, and if you wash it out, the true hand (feel and drape) of the fabric will come through.
2) Fabric will shrink somewhat after washing. You want the shrink to happen before you sew anything out of it, not after your garment is finished, otherwise your finished garment may be ruined when you wash it for the first time.
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