Have a long conversation with your Avian Vet! They are a great source for what you are looking for and to a degree, their recommendations are pre-screened!
The vast majority of the groups you will be looking at are in serious need of a major upgrade to the 501 - 503 status documents and once up to date are open to grants, gifts, etc... My point here is; provide them a fish and they can eat for a day. Provide them the knowledge of how to fish and they can eat for a lifetime! So, yes it is great to go in and help for a while, but why not provide them what they truly need, a revenue stream that will allow them to not become yet another News Story!
Everyone dislikes the paperwork! Therefore, near everyone one of the groups you are thinking about will need help with the paperwork, since everyone is busy doing the fun stuff! Yes, you can still do the fun stuff, but what you will provide on the paperwork side (yes, far more then the IRS stuff) will assure that you will have an endless list of those groups calling you!
Starting with the IRS and State government stuff will help with developing their comfort level in you prior to getting them up and running on the other more personal documents (Accounting 101)!
Remember, near everyone dislikes the paperwork!