Polarizing filters will remove reflected light from windows, water, etc. It will not do that with metal reflections. It will also intensify the blues in the sky.
It's effectivness will depend upon the angel of the sun to your subject. 90 degrees is the most effective.
The best way to select a filter is to find the mm size of your largest lens and get it in that size. Mine is 77mm so I got that size.
For smaller lenses you can get step-up rings so it will fit the filter. This is a good idea for any other filter as well.
I would not buy the cheapest one you can get. You will regret it and in the end buy a better one anyway. Buy the best you can afford. B&W, LEE, Singh Ray, etc.
IMHO, the polarizer is the first and main filter you should get. Make sure it is a "Circular" polarizer.
PS - I just realized that you don't have a DSLR so the size issue is moot. Just get it in the size for your camera.