An Arduino board would certainly be a good place to start, they are low cost and provide a very accessible way to interface Matlab with external sensors and actuators. I'm doing something similar at the moment, but driving steppers in a delta robot arrangement rather than a Cartesian XYZ application.
The Adafruit motor shield is a good little device (I have one here), but it will only handle 2 steppers, so is no good for your purposes. As Rolfe suggests though, it's a cheap and easy way to start controlling actuators via Matlab. There's a decent webinar in the Mathworks library showing how to use it, so you could watch that for an introduction. Link here:
I don't know your application (and I'm no expert, just a student) but a possible solution would be an Arduino, three Pololu stepper drivers, your motors and power supply. Matlab will communicate with the Arduino via a standard serial object. A small C script can be written and run on the Arduino, so that it simply watches incoming serial data, reacting to instructions fired in from Matlab, sending the direction and distance (number of steps to rotate) signals onward to each of the motors.
Take a look at this page:
That article demonstrates something very similar, but driving servos instead of steppers, and sending signals from a Python script instead of Matlab - the principles and the code are very close.
The Pololu stepper drivers are one of the default choices for this kind of introductory stuff, they're cheap and reliable and there are plenty of tutorials online showing how to use them. Beware that they will handle up to 2amps per coil, if you want to drive motors that will demand more, you'll need to look elsewhere (and spend a lot more money):