I am currently knitting a child's sweater (my 1st in 20 years!) with Plymouth Fantasy Naturale 100% cotton 4 1/2 sts = 1" on sz. 8. It is a gorgeous soft yarn, has some give, very nice to work with -- comes in gorgeous colors AND is machine washable.
I have also Lilly cotton (worsted weight) to crochet a child's sweater, and some fingerweight cotton, that i bought from a weaver, for a baby sweater.
I love working with cotton and think any of these would work for a purse.