The stepper driver looks OK. You need a 12V supply for the stepper motor driver, not a 5V one. The Pro Mini version of the Arduino isn't the best choice for you because it doesn't include the USB port for programming or the 5V regulator (so that you can run the whole thing from the 12V PSU). So I suggest:
Arduino Leonardo or Uno
Stepper driver - the one you already linked to
12V 1A or 2A power supply
You can use up/down push buttons. Depending on the mechanics, you may not need end stop switches, if you adjust the motor current so that the torque is low enough not to cause damage when the table reaches its upper and lower mechanical limits.
Two warnings:
1. Set the current using the potentiometer on the stepper driver board before you connect the motor for the first time. To do this you will need a multimeter, to measure the voltage on the potentiometer.
2. Never connect or disconnect the motor to the stepper driver with power connected.
Arduino Leonardo or Uno
Stepper driver - the one you already linked to
12V 1A or 2A power supply
You can use up/down push buttons. Depending on the mechanics, you may not need end stop switches, if you adjust the motor current so that the torque is low enough not to cause damage when the table reaches its upper and lower mechanical limits.
Two warnings:
1. Set the current using the potentiometer on the stepper driver board before you connect the motor for the first time. To do this you will need a multimeter, to measure the voltage on the potentiometer.
2. Never connect or disconnect the motor to the stepper driver with power connected.