A polarizing filter is mainly used to reduce glare and reflections. They also make the sky more blue. I think if you looked on Wikipedia you would find a pretty good explanation of how they work and what they do. A polarizing filter, IMHO, is one of the few filters you still need nowadays - i.e. they perform a function that absolutely cannot be done with an image editor in post-processing.
Sine you have a DSLR, you will have to buy a "circular" polarizer, not a "linear" polarizer. They both are round - the "circular" word indicates how it is made and works. Unfortuantely, circular polarizers are quite a lot more expensive, but that is what you need for a DSLR.
As far as UV filters, they perform a minor function of removing haze, I think, but their main purpose is usually to protect the lens from scratches, etc. There is A LOT of arguing about this idea - some people use a filter to protect their lenses, others don't. I used to be one who used a filter, but I have changed my mind about it and now do not use one for that. I found that they did in fact degrade my images, so I stopped using them, but as I have said, it is arguable.
You cannot use a polarizing filter as a full-time lens protector (as you could with a UV), because it is too intrusive (you only use it when you need it).
One thing I can definitely say - you need to get a high-quality UV filter if you are going to use it to protect your lens. The lower-priced ones definitely degrade your images. I don't mean a particular brand - I mean you need to get one of the higher-grade UV filters of any brand.
With a circular polarizer, it may not be as important to get a super-expensive one, since even the cheaper ones are still pretty expensive and fairly good quality($40-50), and you usually only use them occasionally. Just my opinion, of course.
