how to choose neutral density filter?

The 18-55 takes 52mm filter, The 70-300 either 62 or 67mm, depends on which one you have.

The digit behind nd is usually how many stops difference it's going to make.

The reduction in light depends on what you need to use it for. I have two ND filters. A ND 16 (-4 stops) and a ND 400 (8.65 stops). I use the ND 16 if I want to take a photo of a silky smooth waterfall, as I have found it works the best for me. The "sweet spot" for taking these kinds of photos is around 1/4th to 1/15th second. Any more than that and the blending will become too excessive. And the ND 400 is a special purpose filter, used for photos of solar eclipses. Also, the standard polarizer will give you a -2EV, which is essentially like a ND8 filter, so with the three filters, I pretty much have the coverage I need. I always buy 77mm filters, as professional lenses typically use that size (and I have a couple of them). And I use filter step rings to fit the other lenses, as trying to buy filters for each lens size would be ridiculously expensive. Just the ND400 is over $100 (Hoya ND400) in the 77mm size, so they are not cheap.

Here is an explaination of ND filters:

http://www.althephoto.com/concepts/filters.php

You buy a filter according to the filter size your lens requires (in mm), then how much light you want to reduce. They are listed in EV (exposure value).

So for example, a 58mm ND8 would fit a 58mm lens thread, and have an exposure value of 1/8. which means it lets in 1/8th as much light (-3EV).

Each EV lets in 50% less light. So a ND2 will let in one-half, or 50% as much light (-1EV), a ND4 one-fourth, or 25% as much (-2EV), a ND8, one-eighth, or 12.5% as much (-3EV), and so on.

While the numbering scheme seems a bit odd, if you realize that light behaves due to the inverse square law, it makes sense. The inverse square law is based on the power of 2.

55mm Nd Filter