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.