Welcome to the site. I'm a firm believer in getting the best you can afford when it comes to photography equipment. This includes a polarizing filter. Why put a cheap piece of glass in front of an expensive lens? I have a B+W polarizer that I'm very happy with. I don't have any problems with fingerprints on mine, but that has nothing to do with the filter. It's how you handle them. If they are hard to get off, don't put a lot of force into it. When you grab them with your finger tips, you are creating preasure points that will cause the metal part to change shape slightly, causing the filter to bind which is what is making it hard to come off. The easiest way to remove the filter is to wrap your thumb and index finger around the outer edge of the filter and unscrew it that way. Think of it like using a strap wrench.

As far as the Nikon filter fitting on your lens, as long as your lens has 67mm threads on the front, it should fit just fine. I don't know what the quality of the Nikon filters are like, but I'm guessing they are pretty good.