Puritan males wore their hair long in what you would think of as an American colonial style. Younger men's wigs should be able to be pulled back in a pony tail. Older men's wigs can be more free-flowing with shoulder-length curls.
Puritan women are most commonly portrayed with their hair pulled up in a bonnet. A theatrical wig for a Puritan woman should consist of long curls, which can easily be tied on top the head to be held in place by a costume bonnet. Curls are representative of the reproductive age. Straight hair is used to portray children and older maids.
Puritan male children wore their hair long and usually parted down the middle. Their wigs should resemble a less styled version of the adult male wig. Puritan female children, like other women, wore their hair in bonnets. Their wigs should portray straight hair, or be lightly curled, if the character's age is near adolescence.
Depending on the scope and plot of the production, it may be useful to incorporate other styles of wigs from the time period to create a sense of the socio-political landscape. The barrister wig, for example, is what you would think a colonial magistrate or judge would wear and represent a political and judicial system that is outside the Puritan's realm, as they were not a part of the political elite. These wigs are pure white and dominated by long rows of curls bunched tightly against the head.