New to lens filters..

We can cover a couple of the main filters you will see sold...
1. UV filters - These are more important in film photography, current modern DSLRs do a good job of filtering out UV rays. UV light introduces haze to imagery. Skylight filters reduce blue cast when shooting a clear blue sky. Both of these filters are marketed as a way to protect your lens (more on this later).
2. Polarizer - For DSLRs you would want a circular polarizer, you can use these and rotate them while on the lens to reduce reflections and glare, very useful when photographing glass or water. They also will also work well for landscapes as they darken sky's and other colors will tend to pop.
3. Neutral density - these act like dark sunglasses for your lens, they will allow you to slow shutter speeds down and creat motion in the frame, when you see images where the flowing water has become a smooth creamy mist showing the motion of the stream, this is what they use.
4 Graduated filters - filters with only part of the filter having the change applied to it. These have soft and hard transitions between plain glass and the filter to apply. You can use these in creative situations but an easy example is toning down the sky of sunset image while the foreground is left alone.

Honorable mentions: Tinted filter apply color casts this can be done on purpose for creative needsr, close up filters magnify an image providing a cheap or partial macro ability.

On the topic of filters, they are glass or plastic in front of the lens, even clear ones like a UZ filter can impact an image, possibly soften it slightly. If you buy cheap plastic filters you may notice the image is softer or has an odd color cast, higher quality glass filters should not.
You don't need a UV filter to protect your lens especially if its not a quality filter, so gauge the price accordingly. I have some decent mid priced UV filters I put on when I am somewhere really dusty, otherwise I only put on a filter when I want a desired effect.

 

The UV would be helpful for film, all the rest apply to digital or film, you may want to read up on the difference between a linear and circular polarizer. Some filters lend themselves to the film like a red filter for infrared film. You may want to do some of your own research for the colored filters.
You do not need to get these for all your different cameras and lenses. Some like a CPL or a UV Haze you can pickup a few of them in your most common filter screw on sizes, for example I have a bunch of lenses that take 77mm filter. You can get step up rings to mount a larger screw on filter cheaper than buying another one. For example you can step up a 52mm thread size on a lens to 58 and mount a 58mm filter on it, this is helpful if you have an a few one off thread sizes across your lenses. I have a bunch of camera systems and lenses, so I can definitely say there is no perfect answer. I would start with your favorite or most common lenses and build out from there. You can also make a chart of all the thread sizes for each lens so you know which sizes are the most usable.
I also invested in a filter system from Lee where I can mount a holder to the front of both my EF lenses and my medium format lenses easily and then drop in rectangular glass filters. But that is another level of investment altogether.

 

Yeah I generally trust B&W but Hoya and Tiffen make alright ones if you want to save a few bucks. ( i have a few of theirs.)