You just answered your own question, there is no hard and fast rule for appointing leaders from Quran or Sunnah.
prophet appointed a huge variety of people ranging from muhajireen to ansar to ex-enemies as leaders of expeditions. But Prophet himself was the supreme leader at that time so there was no need for someone to organize the affairs of the Ummah , as it later became an issue after his death.
What was Prophet's solution for this issue? Did he present any at all or left it for the future genrations to decide for themselves?
And since in sharia, the center point is the book of Allah, what does Quran say about this issue of choosing a leader? Any verse, any examples?