Petticoats can be made of gathered chiffon, which tend to stay poofier longer, or layers of gathered tulle, which tend to deflate after a few wears and often need to be layered one on top the other to get the desired poof. Organza is another possible material that, while heavier than chiffon, is stiffer and adds more volume to a dress.
Petticoats should never be worn as a skirt and should also not be longer than the skirt they are being worn under. It's generally considered best for them to be a couple inches shorter than the skirt they are worn under for maximum effect.
Sweet Rococo sells a lot of petticoats as well as Bloomers. Another brand that sells a lot of quality petticoats and undergarments such as petticoats is Fanplusfriend Garden. Another popular brand that sells good quality petticoats with a lot of volume is Classical Puppets.