Ranks are decided by your total number of points. You must have a certain number to advance ranks. You do NOT buy ranks. Ranks are simply based on your point total.

Rank 0 - Starter Rank. Everyone is this Rank to begin with. Requires no points.

Rank 1 - Requires 15 points.

Rank 2 - Requires 50 points.

Rank 3 - Requires 100 points.

Rank 4 - Requires 190 points.

Rank 5 - Requires 310 points.

Rank 6 - Requires 460 points.

Rank 7 - Requires 800 points.

Rank 8 - Requires 1500 points.

Rank 9 - Requires 2250 points

Rank 10 - Requires 4000 points

There can only be ten Rank 10's of each class {Ranger, Mechanic, Operator} at a time. If there are more than that, the top ten will be decided by who has the most points. The top ten are always competing for a better position, so do your best!
Also, don't worry about the huge figures attached to really high ranks. As you advance, the rewards for missions becomes proportionally as large.