The bottle you use for the clay project will not come out . . . sorry! You could just have your kids form their own vase, bottle, or pot if you can't find a bottle that is the right size or shape for all of your kids. If you do use the bottle, you have to use air-hardening clay, though. Don't bake the clay and the bottle.
I have not had great luck in baking any kind of clay without it cracking, in large projects, that is. The best baking clay I have seen is the Sculpey modeling compound - which doesn't crack when you bake it unless it is a really large object. My friend, Robin, teaches elementary school art and this is what she uses and loves. If you don't use the bottle, you can go ahead and bake your Sculpey vases/pots. In fact, you HAVE to bake it or it won't dry (we tried this and about 5 years later we have a model of a Mesopotamian Ziggurat that is STILL soft!)
Regarding the color, you have seen the reddish colored pots and vases in your books on ancient Greece. I don't know why you couldn't just use any light colored clay and paint it a terra cotta color after it has dried. Then paint a design with black after the terra cotta is completely dry.
I am sure others will help you out in reference to where they got their clay, but if you don't have an arts/crafts store near you, the S & S Worldwide catalog carries clay, as well as all sorts of other WONDERFUL things for homeschooling moms.
S & S Worldwide
PO Box 513
Colchester, CT 06415-0513