I will not list every single officer as the majority of them you gain just by completing the story missions. I will however list the tricky ones. Another thing to keep in mind is that certain officers won't join you if you have certain officers in your group. Such as when i was trying to get lady Noh. For the life of me I couldn't get her to join and I was sure I was doing everything I needed to. I took out Nobunaga and sure enough it worked. So I suggest using the default characters from each faction just to be safe.
I just read on GameFAQs that the situation with Noh is the ONLY instance where your party prevents you from getting a character. Nobunaga triggers a different dialogue. As far as I read, you can use any character to get any of the others to unlock. You may want to change the wording so that people aren't wasting their time fighting with the main faction characters if they can just use their preferred party instead.