I am learning about stepper motors as well. To run a stepper motor from the Arduino you add a "shield". shields will control 1 and maybe 2 stepper motors but I don't remember seeing one that can handle 6, so you may end up using more than one Arduino.
Why do you need six steppers? I can see X,Y and Z axis plus an axis to index lasers but that only makes four, what are the two other axes for?
When the stepper motor is stopped it still draws power but it will hold its position without the need for a brake.
Check what size of step your stepper motor makes. It may step by 1.8 degrees, though micro-stepping may be possible. So, if you want to move by less than 1.8 degrees you may need gearing.
Because the you can count the steps the motor takes you don't need to use encoders to work out your position. That is providing you use the motor within it limits and you do not cause it to jump by applying too much force.
It is worth remembering that mechanical devices have inertia. You cannot move them to full speed instantly or stop them instantly. If your laser system has a lot of mass then you will need to accelerate the stepper motor up to full speed and then decelerate it back down.
That is about all I know. I am not sure how big a motor the shields can handle i.e. how much power the motor can draw.