Before I try to make a Eggbot...

http://www.thingiverse.com/thing:20398 is the design I intend on using I believe.

I have never messed with Arduino board's and such before, or tried to hook something up like this, but it look's pretty fun. It say's I need 2x NEMA17 Stepper motors, 1x 9g hobby servo (Turnigy TG9e or HXT900 is what it was designed for), and it's hooked up with a Arduino board.

Another person who had made it said they bought a EiBotBoard to make it a lot easier to hook up instead of the Arduino board. It's $50 for that, or I seen some different Arduino boards at Microcenter near me for around $20, what's the main difference I'll be facing?

Also, will these part's work, as long as they are in stock I could just pick them up at this store. And other than these, anything really important I would need with it?
http://www.microcenter.com/product/4..._Stepper_Motor
http://www.microcenter.com/product/4...rvo_Tower_-_9g
http://www.microcenter.com/search/se...px?Ntt=Arduino <----I'm not sure which is the exact one I would need.

Thanks in advance, ask if you need more info.

Adafruit has a motor and servo shield that will drop down onto the UNO quite easily. They have a custom library that should make it very easy to use. https://www.adafruit.com/products/1438 If you need more connections for other projects, they have a much bigger shield.

Start with an UNO, as they are the easiest for learning, and make great test boards. You can find UNO mounting brackets on thingiverse, then you can attach it to a breadboard, allows you to protoype. Mega's are for BIG projects, Nano's, micro's, and other are good for projects where weight and size are issues. I have 2 UNO's for light deployment and prototyping, and a handful of Nano's for more permanent projects.

But honestly, I'd go on Amazon or Ebay and get an UNO Starter kit. It'll contain 90% of the items you'll need for most projects, plus it will inspire new projects. You can also find more generic motor shields than the adafruit one, but library support might be spotty. But a decent starter kit and a motor shield (if you want one) would be your best choice.