I am creating a project where I need 16+ (possibly up to 20) servos to open/close liquid flow through tubing, which in turn will be controlled by a peristaltic liquid pump (https://www.adafruit.com/product/1150). Since the adafruit servo shield (https://www.adafruit.com/product/1411) gives you access to 16 servos per shield, it seems like the obvious option. However, this shield wont be able to drive a peristaltic pump. I've been told I can put a adafruit servo shield on top of a adafruit motor shield (https://www.adafruit.com/product/1438), but is this really the most effective way to build this project? I want to have a system that is as compact and cheap as possible, using already-available electronics (although I suppose one option is to build a shield myself, but having not done that before it would take me a very long time).
I am quite new to arduino and its accessories, so I apologise if this is a very simple question.