No you don't have to use a stainless steel pot, some brewers use aluminum. I have used aluminum but now use a stainless steel pot.
Stoneware... I'm not sure but I suppose if you can boil food in it I would assume that you can boil beer in it. But isn't stoneware really porous? I would think that if the pot is used for other things it would hold residue from previous food items and may affect the final quality (taste) of your wort. This is all just speculation, I don't have any practical experience with a stoneware pot.