I had some misinformation on here regarding women's clothing. I was able to talk to Elizabeth Stewart Clark about it and she gave me some good basics regarding petticoats.
Petticoats: two or more is definitely very common. They are usually gathered to a fitted waistband, and hemmed between lower calf and an inch or two above the skirt hem [note: not peeking out below your skirt!]. In the 40s and 50s, petticoats are combined with corded underskirts to give better support. After 1857, hoops come back into popular use, and then the main skirt supports are a modest hoop with one or two petticoats over it. The average ranges for petticoat fullness at mid-century run from a narrow version (130" or so) to quite full (180"), with most falling somewhere between 140" and 180".
I don't suggest using elastic in petticoats. It's far more bulky than a fitted band, and just can't support the weight of a full petticoat as comfortably as a fitted band. And, I've not yet found any documentation for petticoats with elastic banding at the top. Drawstrings are really atypical for petticoats, too. As you've found, they slip! Gathering to a fitted band is the best, most historic option.
While cotton sheeting can be used for undergarments, I do recommend those sheets be white, as that is the most common undergarment color. When undergarments are another color than white, they are generally also wool; natural and red wools show up for winter use, particularly for petticoats and wool flannel drawers.
While some [dress] skirts were recycled into petticoats, white petticoats are also very common. In some working situations, a patterned underskirt is a great option!
Liz has more good info on petticoats and how to make them.