cnc robotic arm (arduino vs raspberry pi)

I want to build a record and repeat robotic arm.
I got the idea from this website:
https://www.youtube.com/watch?v=QVsdaPGUn1o
except I want to use stepper motors with encoder attached to the back shaft.
here are the links to the stepper motors:
Phidgets Inc. ... _id=3330_0
and
Phidgets Inc. ... _id=3340_0
and the encoder:
Phidgets Inc. - 3531_0 - Optical Rotary Encoder HKT22
I would like help on selecting a controller and/or shield hat etc... that would be able to accept the encoder feedback and control 5 stepper motors. If possible i would like to use either an Arduino or raspberry pi. but it would be fine to use some other controller.
I know that it is not conventional to use encoders on stepper motors, but I think that the encoders could be used to record the movement of the stepper motors and then repeat the motion.
I want to depower the motors and manually move the robot arm, while the encoders record the position, then i want to "replay" the motion.
your help is appreciated.