Agree with salmonmac. Cotton’s big problem with sweaters is the lack of elasticity. If you want a fitted sweater, you don’t want to go with all cotton as it won’t be fitted by the end of the day. Something with less shape that already starts out baggy might be OK.
Three ways to deal with cotton’s stretch factor - get a blend with wool or acrylic, knit at a tight gauge and use lighter-weight yarns. (Cotton is really heavy.) Blends with rayon or silk will provide better drape as well.
If you really want 100% cotton, look for mercerized cotton. It’s more shrink-resistant and sturdy. Not to mention, a little silky feeling. Oh, and less likely to shed.
As to the gauge swatch, are you assuming the end product will be tossed in the dryer? Shrinking isn’t likely to be an issue if you’re laying it flat to dry as you would with most delicate knits. If you start with a machine-washable cotton that also says to tumble-dry, you’ll probably be OK. Many still say to lay flat to dry or tumble-dry a little, then lay flat to dry, even if they’re machine washable.
I’d work up a single swatch using three needle sizes, probably two apart, so 4, 6 and 8. Measure before you wash and dry, measure after you wash and dry. Then figure out any gauge change by percentage and use that to decide on your final needle/gauge choice rather than keep making swatches. Assuming they all shrink the same. You might find you get less shrinkage naturally at a tighter gauge.
[I have got to start writing shorter answers! Sorry for the encyclopedia!]