Yes, ponds need filters, primarily for biological filtration and also to keep the water clearer.
Air pumps are fine, but pond pumps are better.
One filter system I use (mini-version) is at the following link, which I built myself for about $200 plus the pump.
http://www.skippysstuff.com/biofiltr.htm
It's not hard to dig 3 to 4 foot deep at all, its surprisingly easy actually, once you get going.
It's say stick to comets and sarransan goldfish for a pond that size, good for starters anyway. Once you get the trick, and re-build your pond bigger (it happens a lot), you can look into more expensive Koi.
My signature (below) has some photo's of my pond, which is a premade 180 gallon system. I store my goldies indoor (about 5' away from my computer acutually) in a 7 1/2 x 2 x 2 foot tank.
Welcome to the tank!