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You'll need 1) 2x stepper motors 2) 2x stepper drivers 3) a motion planner (pulse generator).
The stepper motors 1) are obvious and there are a range of solutions out there that can be used for 2) and 3).
The simplest solution would be an Arduino Nano with Grbl installed connected to two DRV8825-style drivers. This would fit on a single breadboard and cost a few dollars. You could also use a RAMPS board (3D printer mainboard) if you have a surplus one. Or, the most deluxe version, Mach3 on a PC connected to 'real' stepper drivers. Depends on how 'nice' you want to make it.
My setup is a Nano (Grbl) connected to DM422 style drivers. And a Raspi to send gcode over USB-serial.