A cookie becomes crispier, not from just a single ingredient, but more or less from the process on how a cookie is made. If you are looking for crispy, go lighter on the brown sugar since it absorbs more moisture than regular sugar and makes a softer cookie. Also, margarine has more moisture than butter or shortening. The more margarine used, the softer the cookie. Butter has a quicker melting point than shortening, so the cookie will spread more if using just butter. For a good, crisp cookie, bake it at a little lower temperature for a little longer time, to take some of the moisture out.
Btw, welcome to BakeSpace! This is a great site. Be sure to check out the forums---there are all sorts of people that can answer questions on about anything there!