The ranks you can choose from are:
Academy student (Elementary school)
Genin (Middle school)
Chunin(High school)
Jounin (College)
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The ranks that only a certain number of people can have at once are:
Kage (one at a time)
Akatsuki (Only ten slots open)

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Special cases:
Missing nin (Not Akatsuki rank but still a criminal)
Sannin (Only three open, technically)

To claim a Rank the first three are fair game the Specials and Limited Ranks you have to fight the person currently in the position you want.

** Case to the contrary: Akatsuki is a rank you can't just claim I'll repeat that
CAN'T JUST CLAIM!!!!
To claim an Akatsuki position you need to be evaluated by the current leader of Akatsuki or the captain/a crew member. (Note: there will be a form to fill out for that position and you can be kicked out by lack of participation or if the current Akatsuki leader sees fit and takes it up with the Captain of the guild.)