Hi Neil,
I gave a presentation at IISAC 2011 on "Visual Astronomy and the use of filters".
Here is a thread on this which has a link to the presentation which you can download as a PDF
Here is a direct link to the presentation PDF
Don and a couple of others have given you sound advice already.
I would recommend either a DGM NPB filter or an Astronomics UHC as the filter you need to start with. They are both excellent but slightly different, notwithstanding they are both narrowband filters. A H-Beta filter is pretty specialised and has a limited number of targets on which it is useful. As Don suggested you buy this after a Narrowband (UHC) and an OIII. A Narrowband like the DGM NPB or Astromics UHC will provide some assistance to see the Horsehead but not as much as a H-Beta. However, the narrowband will provide a noticeable improvement on hundreds and hundreds of targets compared to a handful for the H-Beta.
Don has not mentioned the Astronomics filters. Many people in the USA don't like them, where as most people in Europe do. The Astronomics UHC filter has a somewhat broader bandpass than some of the other narrowband filters like the Lumicon UHC, DGM NPB, and the Orion Ultrablock. This will fractionally limit the filters ability to eek out the last piece of minute detail in the nebulosity itself, but it gives an aesthetically more pleasing view when viewing emission nebula with embedded clusters, like Tarantula (NGC 2070) Eta Carina (NGC 3372), Orion nebula (M42), Lagoon (M8), Triffid (M20) and countless other targets of this type. The Astronomics UHC because of its broader bandpass lets more of the background stars through compared to the other narrowband filters, while still providing excellent contrast extension of the nebula and many people find these views to be more aesthetically pleasing than the views provided by the UHC filters having a tighter bandpass. The Astronomics also works slightly better on the horsehead than do the tighter bandpass UHC filters. It's all about personal preference, what view you provide aesthetically pleasing and what targets you like to look at. There is no right or wrong answer and one is not better than the other, they are slightly different and do different things and it's all about your personal preferences. I have both a DGM NPB filter and an Astronomics UHC and they both get a reasonable share of focuser time. However, unlike "most" of the tighter narrowband filters, which are made in Korea the Astronomic UHC is made in Germany and it isn't cheap, particularly the 2" version. On that basis I think you should head straight towards the DGM NPB which is an excellent first filter. Just be aware that if $$$$$$ aren't a concern there are other slightly different excellent options available.
Cheers,
John B