I think that this is a dam if you do and dam if you don't situation. I have had the 12-24 for a number of years now. It is one of my favorite lenses. If you choose to go the UV filter route, 77mm one will not be cheap. If you go the low quality route, you will just be diminishing the image quality of the lens. If you go the high quality route, it will be expensive. There are folks who will swear that this is the best action - to have a filter for protection. Then the other half of the population, will swear that it's one of the worst ideas around.
You can bypass the UV filter route and some folks get a polarizer filter to provide some protection. The problem with this idea is that with a lens under about 24mm is sufficiently wide that the polarization can not stretch evenly across the entire image, and thus you will get an uneven application which shows up in the sky - so the results will be part of the sky dark and the other part normal. Also, you really do not need a CPL most of the time.
A bit more reading and you will find that with wider lenses, filters may tend to vignette. So you tend to go with the thin filters, which drives up the cost even higher.
I did get a CPL for my 12-24 - a low profile, high quality (Nikon) and it works very well. The sky does turn out uneven, however I try to find a branch of a tree to break up the sky so that its not as noticeable, or minimize the sky in composing the shot in some way. Here in Arizona, we get so much sun, that the reflections can wash out the colors. That's why I picked up the CPL for this lens (and did pay a price).
Bottom line - just watch yourself, be careful - and like selar said - use the hood.