A standard strength polarizing filter typically will reduce light by one to two stops, depending upon the setting. (There are "HT" or "high transmissive" polarizers that reduce a slightly less... roughly 3/4 stop to 1.5 stops).
Neutral density filters come in a wide variety of strengths, from as little as 1/3 stop to as much as much as ten or fourteen stops. Still photographers usually just need two or three fairly strong strengths to "shift" their exposure range significantly, and then can use other exposure factors to fine tune their exposure, to get the effect they want. Videographers may need a more different strength ND, since they have less flexibility with other exposure factors.
ND filters are often used to allow a slower shutter speed than would be possible without the filter, for deliberate motion blur effects. They also are sometimes used to be able to use a larger aperture than would normally be possible, for shallower depth of field effects.
A polarizing filter can be used as a relatively weak form of ND filters. But polarizers have additional effects... In simple terms, "polarization" works by blocking oblique or scattered rays of light light, while allowing aligned light rays to pass through the filter. This has the effects of reducing reflections, increasing color saturation, deepening the color of the sky, etc. Sometimes for a particular image these are desirable... but for other images the can be unwanted effects. For example, IMO, a polarizer would have ruined the following image, by reducing or eliminating the colorful reflections of the sunset off the water, wet sand and rocks...
For the above I wasn't looking for the "creamy water" effect of a long shutter speed and wanted depth of field from near to far, so used a smaller aperture... For that reason I also didn't use a neutral density filter.
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Get a size that fits your largest lens and buy adapters for your narrower lens so you only buy them once. Same for all filters
I disagree. Step rings make it difficult or impossible to use a good fitting lens hood.... which I consider an important accessory. For that reason, IMO it's better to buy filters in the correct sizes for each lens. But you might only need a particular type of filter with a certain lens... for example I rarely use either a polarizer or ND on longer telephotos. Most often I use them on wide angle lenses, occasionally on normal or short tele lenses. You can prioritize and initially only buy the size and type of filter most likely to be used... gradually add other types and sizes if and when needed.
Besides... with digital only a few types of filters are needed, so it's really not a problem. You no longer need color correction or conversion, warming and cooling, and many other types of filters that were necessary when working with color film. You also don't need the various specialty filters that were used with black and white film. With digital, all the "old school" filter effects and more are very easily done in-camera or in post-processing.
With film I had more than 100 filters... and I mostly used two sizes of screw-in with step rings, to reduce the number of filters I needed.
Now with digital I only carry three types of filters, in four different sizes. So with a few duplicates I now carry 15 or 16 filters, total. I don't use step rings on my lenses, most of which use bayonet or clip-on hoods that wouldn't be usable with over-size filters and step rings. (I do use some step rings to be able to stack filters of different sizes for storage.)