I'll put my two cents in here.
I would really recommend using acrylics for a few reasons. Acrylics tend to dry faster, which makes it easy to do lots of thin layers and get a nice, smooth finish. Oils stay wet for longer, so you may have to keep coming back to paint your pony over a few days. Acrylics are also good for fine detail and crisp lines, which is good when you get on to small scale painting (eyes, symbols).
My personal advice is to go with acrylics because they tend to be cheap and easy to find at a variety of stores. Colorscapr mentioned Createx, which is a super fine airbrush quality acrylic. Their opaque colors are a good choice for a base. I use a lot of Vallejo colors, which you can find at Hobby Lobby or (if you have one) Hobby Town or a Games Workshop type of store. They're cheap at ~$3 a bottle and it comes with a convenient dropper, which is nice when you mix with water.
Edited to remove double post. Thanks! ~ CSA