Need Circular Polarizing Filter-what size fits?

Have a Nikon D90 DSLR that came with an 18-200 lens, a Tamron 10-24mm wide angle and Tamron 70-300 telephoto. Do I need filters for all three and how do I know what size filter to buy? Am told B&W is best but are Hoya filters any good? I use the wide angle for my landscape photography so this is the main one I would use the polarizing filter for.Am fairly new to photography so I appreciate the advice.

No you do not need a polarizing filter for all three

The 10-24 mm is two wide to use a polarizing filter well. 1) the angle of view will cause a huge difference from edge to edge of the sky and 2) you will get vignetting at the 10 mm to 14 mm settings
The 18-200 mm lens can use the polarizing filter under certain conditions, mainly when shooting at 90 degrees to the arc of the sun. You will need a 72 mm filter.
The 70-300 mm can use a polarizing filter, but since the 18-200 mm shoot in all the ranges that a polarizing filter is useful, you only need the one filter

Both B+W and Hoya are excellent filter makers

Note each of your lenses have the filter thread size listed on the lens

On the lens, look for a 0 with a slash mark through it. The number following that symbol is the filter thread size.

Ace is correct in that a polarizer filter on a very wide angle lens will cause "banding" in the sky, (some areas of the sky will be much darker than others). A polarizer is only effective in a relatively narrow band of light. A wide angle lens has a larger field of view than the filter is able to affect. As your camera has a crop factor to the sensor, you *may* not have a problem using the polarizer at the 24mm focal length, but it would be iffy at best.

Yes, B-W filters are excellent, and at a price to match. Hoya filters are a good cost to value alternative.

Note: If your lenses are all different filter sizes, you do not have to buy a ton of filters at those different sizes. You can buy one set of filters in say a 77mm size. You can then buy what are called step up adaptors. These adaptors allow a larger filter to fit on a smaller filter thread. For instance, if one of your lenses requires a 58mm filter, you would get a 58 - 77 step up adaptor. The adaptor has 58mm threads that screw into your lens, and the outside threads are for the 77mm filters. These adaptors can save you a ton of money by allowing you to only need one set of filters regardless of any various lens filter thread sizes. The adaptors can be bought for as little as 2 or 3 dollars each.