Should we presume that you're at home with how to store data on external EEPROM? Presumably you'd need a chip or two of EEPROM if there is a complex series of movements to record. Gramo has a great website that describes how to interface a PIC to EEPROM chips. Here's his link:
Not to oversimplify your project, but just to break it down a bit, it seems to me that you could wire a pot to an A/D pin, a pushbutton to another input pin, and a servo to a PWM pin. Have your program adjust the PWM signal with respect to your input controlling via the pot. When you hold the pushbutton, the PIC records the PWM at any given time intervals (every 20ms seems about right). It seems to me that it'd be good to have that pushbutton recording feature, so that you could do practice runs without the button depressed until you get the motion "just right."