Jersey is a "single knit" and that is why it curls up at the cut edges. It has a definite front (face) and back surface, and will also run from the cut edge with ease. Interlock is a "double knit" which makes it thicker, and will usually lay flat after cutting, does not have as noticable face and back, and usually will not run from the cut edge easily, especially with 100% cotton fiber content.
Interlock does not stretch as much as single knits, but it has some stretch in all directions. Single knits stretch a lot in the crosswise direction but usually little in the lengthwise. Single knits show a definite rib pattern, especially when stretched, and will allow some fiber migration, making it less suitable for use in toys and as doll skin. Single knits may be cut in strips 'across the goods' and used as ribbing for cuffs. Interlock is not suitable for this application.
Both kinds of knits come in many different fiber combinations and 100% cotton is the most absorbent. At $4.50/yd I would be surprised to find out that it was pure cotton, and definitely not a "long" staple cotton, which is the nicest kind - silky and soft, but also strong and resists pilling. Short staple cotton pills quite a lot, but the pills fall off, over several washings Beware of any poly/cot. blends, which stain easily and pill like crazy. The pills will be much worse than even with a short staple cotton, because the poly fiber keep the pills firmly attached. HTH.