Dialogue/conversation/discussion

1) A solution may not yet be in sight, but the important thing was to get a dialogue between them started.

Is the sentence 1) correct?

If 'dialogue' isn't the appropriate word, then can I use 'conversation' or 'discussion in the sentence?

If it's between two parties, then all three are fine.

Dialogues are always between just two, while conversations and discussions can include more.