Nusach is the style of the prayer service practiced in different communities. The differences in structure and melodies (the melodies are also called nusach) are normally relatively minor, but they can be enough to trip you up. When dealing with an unfamiliar nusach, just keep following the siddur. There are many nusachim, but there are three primary nusachim you will find in your run-of-the-mill American community:
Nusach Ashkenaz: the most common in America. There are variations, but Artscroll’s Ashkenazi siddurim are very widely used.
Nusach Sephardi: There are actually many variations according to the particular Sephardi community. There is no authoritative Sephardi nusach like the Ashkenazim have.
Nusach Ari: (You may hear this called Nusach Sfard.) Nusach Ari is a version of Nusach Sfard (also spelled Sefard) used by Chabad chassidim. If someone calls this Nusach Sfard, don’t make the mistake of thinking it is Sephardi. Nusach Sfard and Nusach Ari are very similar to Nusach Ashkenazi but attempt to include kabbalistic ideas and customs. Each chassidic group has its own version of Nusach Sfard, but the Ari is most well-known because of the wide geographic reach of Chabad.
If you want a cool Jewish hobby/hoarding opportunity, consider collecting siddurim!
The chart at http://opensiddur.org/2010/05/a-historical-map-of-jewish-liturgies/ is excellent for those wanting to get thoroughly confused.
As a avowed davener of Sfard, I'd say you should have Nusach Sfard as its own section. There's enough places that daven Sfard, and I have a stories of people who got ambushed by a Nusach Sfard shul.
There's a friend trying to follow along with a Sfard congregation in the LES and giving up. She figured it out when she was talking to someone at kiddush – "That's why the pages didn't match up!"
And there was a guy who was hard of hearing and saying kaddish while visiting Portland who had the rabbi come up to him after ma'ariv and asking him while he kept barreling through kaddish (since he was a sentence ahead the other people who were saying kaddish).
You should definitely distinguish between Nusach Sefard and Nusach Sephardi.
I recommend Rabbi Adin Steinsaltz's Guide to Jewish Prayer, which has a chapter on different prayer rites (nusachim).
I want to correct your error, in saying "Nusach Ari is a version … used by Chabad chassidim"
The 1st Rebbe of Chabad had, in his time, 60 versions of Nussach Ari. What he did was, he took them all and reconstituted them into nussach Chabad – in such a way as – no matter who you are, using this nussach will give ascent to your prayers.
That nussach parallels the 13th gate in Jerusalem. Every tribe had its own gate from which to enter and exit. A Jew from one tribe could not use the gate of another tribe. But there was the 13th gate, through which all or any Jew, no matter from what tribe he derives, can go through.
The Sephardic nusach is called "Nusach Edut HaMizrach", rather than "Nusach Sephardi".
I do collect siddurim; it's really fun! -Ezra
Edut HaMizrach would be mizrachi, not Sephardic, right?