Well first your going to need a power source (battery). I assume you want this to last for a game or two of golf before you want to charge it again. A lithium ion or small sealed lead acid battery (more weight though) should do the trick.
For motion, you can use two small wheelchair or scooter motors (http://www.monsterscooterparts.com/
I highly recommend differential (tank style) drive with a off road caster (for all those times you hit it in the rough
In order to drive and control the motors, you'll need a motor driver. Check out the Sabertooth from Dimension engineering. If that's too expensive, there are plenty of other ones cheaper. The Sabertooth is high quality though, fairly easy to configure, and there is plenty of documentation on it.
For MCUs, I recommend using an Axon or Arduino. There is a ton of documentation on both.
If you want remote control, just search "rc transmitter and receiver" on google and you should find many options. Plus the Sabertooth has an rc mode that is really easy to set up and configure.