I have a project which when complete will attempt to build an online community with features specific to my favorite hobby. The project has been designed such that eventually we can extend this project to other hobbies and small communities. We have chosen this particular hobby because 2 out of the 3 people working on it are deeply involved in the community around it and hope to translate that into features which collect the most useful information being generated as the hobby progresses.
Our chosen audience is very small however. In the US alone, there are fewer than 10,000 active participants in the hobby and only a fraction are active in online. Having spoken with a number of key people in the community about the value we could create for them, and hopefully in turn build revenue streams off of, the project seems like it would be self sustaining with a small (3 to 4 zeros) yearly profit. Take that with a grain of salt as I have little venture experience and might not completely grasp what self sustaining means today versus two years from now.
Would it increase our chances of success to focus on a larger audience earlier on? Success: we don't give up on the project and create a few thriving communities.
I'd say that actually your involvement in the target community is what can make your service successful; you have domain knowledge, and most importantly know how to promote it and what are the best strategies and places to introduce it to the community. So my suggestion is definitely to start in the small niche.
Having your service out, and active users (even a small group of them), is the best way to understand how to change and evolve the product. Only after you tuned it, and you are sure the service is useful and engaging, I'd try to go for bigger communities.