[Don Pensack]

There are basically 4 filters that make sense for the amateur looking at nebulae:
1) Broadband. Also inaccurately known as a light pollution reduction filter.
This filter slices out a chunk of the spectrum in the yellow-red area of the spectrum to reduce the glow of the atmosphere from artificial lights. Unfortunately, the effect is relatively minor unless you are already under really dark skies. Even there, the effect is like turning up the contrast a tiny bit. In strong light pollution, so much light bounces around inside the filter that they often make sky glow worse.
Examples:
Orion SkyGlow
Lumicon Deep-Sky
Baader UHC-S
2) Narrowband. This reduces transmission to only a narrow section of the spectrum where nebulae emit energy: Hydrogen emission and Oxygen emission. The Hydrogen emission in the deep red is almost beyond out dark-adapted vision, but there is also a hydrogen emission in the blue *486nm), and the Oxygen emission is nearby in the blue-green (496nm and 501nm). The improvement in contrast is amazing. If you get one filter, this is the one to get.
Examples:
Lumicon UJC
DGM NPB
Orion Ultrablock
Thousand Oaks LP-2
TeleVue Nebustar
3) Oxygen-III filter. Narrower than a narrowband, the hydrogen emission line is eliminated. It improves contrast of small areas of a nebula that emit light in the ionized oxygen wavelengths. Excellent on planetaries and some supernova remnants.
Examples:
Lumicon O-III
Orion-O-III
DGM O-III
Thousand Oaks LP-3
TeleVue O-III
4) Hydrogen-Beta filter (H-Beta filter). Narrowest of all because it restricts transmission to only the 486nm line of Hydrogen Beta. This enhances the secondary ionized hydrogen emission, and makes some very faint hydrogen nebulae more visible (example: IC434 behind the Horsehead Nebula, The California Nebula in Perseus) There are only a handful of objects where this filter is best, but it can do a good job on them.
Examples:
Lumicon H-Beta
Thousand Oaks LP-4

In order of how I would acquire them:
1) Narrowband. The most versatile and "universal" of all the nebula filters.
2) O-III filter. Useful on almost all the objects with strong O-III emission.
3) H-Beta filter. (If you have money burning a hole in your pocket)
4) Broadband filter. If you view at a really dark site and just need to tune up the contrast a bit. If there is any advantage to this filter, it is that it can be used at a little higher power without making the field too dark.

The best magnification to use the filters is 10-12X/inch of aperture and down. Otherwise, the objects may tend to get too dim.