Well, this thread looks dead, but for posterity...
I have several years experience building large-scale enterprise applications. In my experience:
* Git: Yes. Branching is a very good thing. Dead branches are the best place to put false starts anyway and often provide inspiration for new branches. Not everything makes it back to master, and it shouldn't.
* Issue Tracking: Yes. Github can provide some of this. Even their simple issue tracker keeps things moving along and all major open source projects (think Apache Foundation) use issue tracking and release management.
* Nightly builds: Yes. Jenkins is fine and Travis integrates with Github for a small fee. As a non-profit, it would probably be free. This is one of the best ways to enforce good coding practices.
* Unit tests: Well, duh, yes.
Another thing, issue tracking allows people (like me) with an interest but not a lot of time to jump in and participate. I asked how to contribute the other day and there were only "big lifts" available. The new generations of developers (whom it would be nice to attract) think in terms of agile build/deployment cycles, issue tracking and code review. Those are good things.
Thought I haven't the time to manage it, I'd be happy to participate in both product and project mgmt, and throw in some code now and then.