It’s probably not very practical to use the Phidgets stepper motor you mentioned with any of our stepper drivers. That motor uses more current than any of our stepper motor drivers can provide so the torque available from the motor would be well below its potential.
The Arduino Uno and our A-Star boards have a lot of similarities, however there are some specific differences between them and, in general, we cannot say which might work or be better for your application. You have several questions about interfacing other boards and one specific difference between the Arduino UNO and our A-star boards that might be relevant for your application is that the ATmega328p microcontroller the UNO uses only has a single hardware serial port it can use to either talk to a computer over USB (like you mentioned for MATLAB) where the ATmega32U4 microcontroller the A-Star uses has a dedicated internal serial port for communicating over USB and an additional hardware serial port that can be used for a hardware peripheral like the Maestro.
To determine whether any combination of other devices might work with your microcontroller board, it helps to think about how each device connects to the microcontroller and to look for potential conflict between those connections. For our DRV8825, we provide a Minimal wiring diagram on the product page for the driver that shows a minimum set of connections. Our Maestro user’s guide and Tic user’s guide (both linked to on the “Resources” tab of their respective product pages) document the connection interfaces available.
It sounds like the devices you want to use will require a range of different voltages. You can find our AC power adapters (which will allow you to get low voltage DC power from an AC mains plug) and our voltage regulators (which can convert from one DC voltage to another) in the Regulators and Power Supplies category on our site.
We do not know of any 6mm shaft couplers for the servo you mentioned.