Unless you are clumsy type and are interested in a filter or filters for your camera. Start with a circular polarizer. Like said above it helps to improve pictures by blocking polarized light from the sun. It will help turn a dull blue sky into a nice dark blue sky. Or say your are taking a picture with glass or water in it. By turning the filter you can either allow light to reflect off the glass or go away so you can see through the glass or water. It is the most used filter I have (I have a couple sizes for different lenses). There are two types of polarizers. Circular and just plain polarizer. They do the same thing, just the circular one, the glass element can rotate without loosening the screw mount to the lens. Basically for more money its easier to use. To use a polarizer you turn it until the affect you want (goes from full effect to no effect in a 1/4 of a turn).
Now if you are clumsy or afraid you might damage your lens. Alot of people keep a UV filter in front of their lens for protection. They don't change the scene very much and are fairly low cost. There are different qualities of filters. Cheap ones may be made so bad they affect the pictures in bad ways. So be carefull in choosing them. You don't have to get the most expensive one. But like in anything you get what you pay for. Cheap ones may be just fine if you don't do large enlargements or prints. But they may start to show bad things with large prints.
Also stacking filters. There is no rule against stacking different filters. But normally you just use 1 or 2 at a time. The more glass layers you have in front of your lens the lower the picture quality will come out. And if conditions are right you may get stray light reflections off the additional glass and ruins the pictures (bounces around off the different glass layers).
There also filters wher maybe only half of the filter has a shade or color. This is a special filter to help with specific scenes. Alot of colored filters are used for filtering out certain light. Like for shooting b&w lot of people use a yellow or red filter.