building a motorized timelapse camera slider

I am trying to build my own motorized camera slider instead of buying a professional rig. What I'm trying to figure out is what pieces I will need to accomplish this. I'm looking for something that will allow me to run different code programs from the device itself so that I can make the slider move at different speeds.(Something like a Lego mindstorms nxt intelligent brick) but cheaper. I a newbie at this kind of stuff and really appreciate any help. With some help from the internet I came up with this.

Currently in my designs I am planning on using these items:
Nema 17 12V Stepper Motor
Arduino uno R3
12V battery
Spark fun Big Easy driver
Adafruit LCD Shield kit for Arduino
Arduino Adafruit LCD Case: to keep it safe
There are more mechanical pieces not listed because they aren't important for this forum (camera dolly, gear, rope etc.)

My questions are:

  1. Do I need to use the Spark fun Big Easy driver if I'm only using a 12v battery or can the arduino handle that much voltage?
  2. Are there any pieces missing?
  3. Will using the LCD shield kit allow me to choose which program I want to run with the arduino?

Possible info.

wow thanks! there's a lot of great information there.

You may also be interested in stepper motor basics

Note that "Nema 17" says nothing about the electrical characteristics of a stepper motor.