One easy avenue available is to get 4 continuous rotation servos and some wheels that can be mounted to them. For example, four of these:http://www.robotshop.ca/roboblock-continuous-rotation-servo-wheel.html
They can be driven (though not powered) directly from an Arduino, and they can usually be powered from the same power source as the Arduino.
If you go with 4 separate motors for drive power, then you are also going to have to get a motor controller that is capable of driving those 4 motors. It'll be more expensive and more complicated to set up. something like:http://www.robotshop.ca/solutions-cubed-ezr-5.htmlhttp://www.robotshop.ca/solutions-cubed-easy-roller-robot-wheel-ezr2-1.html
could be used, but require a motor controller to drive them, something like:http://www.robotshop.ca/Sabertooth-2x5-en-5.html
That latter setup would have a higher payload capacity and higher top speed than the servo setup, but also a higher cost and higher learning curve. Being a novice, I'd recommend the servo route, and upgrade when you outgrow them (also, continuous rotation servos have other uses within hobby robotics, so you would likely be able to repurpose them if/when you outgrow them, as opposed to just tossing them aside)
As another option, either setup can also be reduced to a two-wheel arrangement with a caster wheel to reduce the costs by 30-50%.