I have a bit of info gleaned from a couple of books:
Jerseys and single knits both tend to curl. They are often, but not always, light weight and drape nicely, especially a rayon jersey for example. Jersey curls to the right side...it has vertical ribs on the face and horizontal loops on the back. Runs from both ends.
Interlock knits tend not to curl. Not as stretchy as jersey and single knits. They have lengthwise ribs and look the same on both sides. Run resistant. Almost no lengthwise stretch, but stretchier crosswise than jersey or double knits.
Double knits look the same on both sides, fine lengthwise ribs, and do not run. Edges do not curl.
I have quite a few fabric books, and this info comes from two: Threads Sewing Guide and Fabric Sewing Guide, 2nd Edition, by Claire Schaeffer. I have her first edition as well, but the new one is much bigger and I found a lot of new, good info in it.
If you have a knit fabric that you like and want to use, you can minimize the curling by starching the edges, or by applying narrow strips of fusible weft (knit) interfacing. Pre-shrinking may make the curling worse, but of course you need to decide how important pre-shrinking is to you!
I am reasonably sure that those really nice "baby knits" that Martha used to sell...the onesies, sleepers, blankets, bibs, etc., were cotton interlock. My local store also sells a nice poly/cotton blend interlock. I think it is 50/50. I prefer to use the all cotton, but the one I can buy locally is a very nice quality, doesn't curl, nor run easily, and is easy to work with.