Let’s start with when you need a neutral density filter. A normal ND filter cuts down the amount of light going through the lens. You want to do that when the light is too bright to get a slow shutter speed you want, like when you want moving water to look milky. Or when you want to use a large aperture, like f/2.8 on a sunny day to limit your depth of field. People shooting video frequently use an ND filter so they can shoot at 1/30th shutter speed to get normal looking video.
There are a couple of different ways to accomplish neutral density. One is to use a variable neutral density filter, the other is to use a filter that has a fixed amount of density. The variable is much more expensive and gives you more precise control. The fixed is less expensive but you may want two or three to meet all your needs.
If I want moving water to look milky, I usually like to have a shutter speed of two seconds or longer. So if I am shooting 100 ISO and it is sunny, my exposure will be f/11 at 1/125 sec. So I need eight stops of ND to get down to the two second exposure I want, which is why the only ND I carry is 8X.
OK, I kinda lied. I made my own variable ND filter by using two polarizing filters and reversing one in its frame. I can then stack the two on my lens and vary the amount of light coming through, which is how an official variable ND filter works. But I don’t find that I need to do that very often, my 8X ND covers what I usually want to do.
And there are graduated ND filters where part of the filter is ND and part is clear. These are great when the sun is below the horizon and the foreground is dark and the sky is bright. You can cut down the light in the sky but not the foreground. I have to admit that I don’t use my graduated ND filters much any more since Lightroom does such a great job creating the same effect. But I’d say that it is better to do it with filters than software if you are real fussy. They also make slotted ND filters that cut down the light in the middle, like after sunset when the horizon is bright but the sky and foreground are dark. And there are tinted ND filters, but they are gimmicks to me. If you want your scene to be blue or warm, just do it in the computer.
My suggestion is to start with a 8-10 stop ND. You’ll want to have it available for each of your lenses, you never know if you are going to want it with wide angle or telephoto. So either buy one for each lens or buy one for the largest filter size you have and get step-down rings that let you put the larger filter on the smaller lens.