Which Arduino for 7 stepper motors?

I'm building a motion control system for stop motion animation cameras and I'm wondering which Arduino I should choose. This isn't my first electronics build, but it IS my first Arduino project and I'm diving in head first. There's a lot of options and a bit of terminology for me to pick up on. Let me elaborate what I'm planning.

My system is built on a stage and is basically a camera slider on a camera slider with a scissor-lift platform where the camera is mounted. This allows for linear movement along the X, Y & Z axies (that's Dolly, Truck & Pedestal in camera speak and needs the most torque). The camera Tilts & Pans and the camera itself has a dual focus system requiring these two motors to be very precise. All these motions need to be very small increments and, once I have it all working, I'll need to figure out how to replicate them in software like Blender if I do any kind of green screen effects. So, I would build a routine for the camera motion of each scene and increment each motor together with a button on the computer's keyboard to capture one frame. Then, press the key again to advance the system and capture the next frame and so on.

I know this is a pretty complex project and will take a lot of work and plenty of parts. I'm planning to take it one step at a time (heh, pun intended) and get one motor functional, move on to the next, etc. Then, think about the rest.

Right now, so I can start getting my hands dirty, I just need to know which Arduino can handle what I'll be asking of it and any recommendations for a stepper motor & driver + power supplies. Also, if I'm forgetting anything. I have jumpers and breadboards.

Thanks for any advice I can get.

The first step to choosing a stepper is to measure or calculate the torque required of it. Then you can, intelligently, choose the motor. Once you know the motor specs you can select a driver and power supply suitable for the motor.

Steppers do not know their positions so you need a way to "home" each one at start up. That means a limit switch or the like for each motor. 7 motors means 14 pins for step and direction outputs and when you add homing an Uno runs out of pins unless you resort to shift registers or port expanders. A Mega probably has enough pins.

Stepper basics.

When considering 7 motors you should try to estimate the maximum number of step-pulses-per-second that the Arduino will need to produce for the combined movement of the motors. Moving 7 motors at the same time all at high step-rates might be too hard for a 16MHz microprocessor.

Of course it may be that your project does not need all the motors to move at the same time.

...R
Stepper Motor Basics
Simple Stepper Code

also look up the AccelStepper library

While I agree with the above posts regarding pins and capacity, I'd suggest that you start with a basic Arduino such as an Uno and experiment.

It'll be cheaper to replace if you let the magic smoke out and it'll demonstrate whether you need something bigger and faster.