Motor for project

I am making a project for a class. Right now I am using vex parts and a vex 393 motor. I plan on changing everything to Arduino and I'm not to sure which parts to use. I've been looking for a motor but I'm not sure what is compatible with an Arduino Uno. I have found a few 12v motor but I'm not sure if the Uno can handle 12v or how exactly to wire it up. I saw a video where a guy used an external power source and a L293D chip to sire a much smaller motor up to an Arduino Uno but I'm not sure if this approach will work with a 12v motor.

You told us a lot, but very little about what the motor is for.
Slot cars have 12V motors, but I'm pretty sure my full-sized car has a 12V starter motor.

This motor will be attached to a gear that will spin a connected belt. On the belt there will a long wooden rod sticking put that shouldn't weigh much. The basic idea of this project is a device that will knock down items that get stuck in vending machines . The motor will move the rod on the belt up and down to knock the food.

I would not bother with the L293 chip, it will drop the voltage 2.8 volts before doing anything. Determine how much current the motor pulls then get a driver with MOSFET outputs that can handle the locked rotor current of the motor. If the motor does not reverse then a N-Channel MOSFET would do the job. The UNO cannot drive a motor of any type it will be damaged or destroyed you must use a driver. Also a Power Supply the Arduino is NOT!

Does your motor need to reverse?

yes they will reverse

Would I need a mosfet if I used a vex motor

No you would not need a MOSFET for a Vex motor but you can use them. Vex from what I can find makes a lot of motors. Driving it is like buying a pair of shoes, to small and it will not work and break, to big and you can get buy.