Lots of things to consider...

First, a servo is just a motor with position feedback, the feed back circuit will keep the motor or move the motor to a "position". The feedback circuit can be in the motor housing or not.

Stepper motors will also have 4,6,8 wires. Are you looking at servos or steppers?

But for your project you do not need either one. A "regular" motor will do if all you want is full open or full close. A sensor, limit switch at each end will work for feed back.

Then you need to know the torque required to move the door is a worst case scenario. Wear and dirt will change things.

Simple relays will work between the PIC and motor for control, how many amps? The PIC can be most any of them but we will need to count I/Os. Still a few things to add...

Lets assume a DC gear motor for torque and speed. The motor can be turned on and off and direction control through the relays and a PWM can be sent through the relays with a mosfet or IBGT for speed control.

You may also want a sensor to check for obstructions when the door is near closed.

A magnetic switch can be used for door position also. One could be place near full open/close to toggle a pin for speed change. PWM changes.

Sorry for not giving direct answers, but there are many things to consider for the total design.