It's a little confusing with the terminology, but the player with the lowest fleet total has "initiative," or whomever wins a coin flip. Then the player with "initiative" can choose to either be the "first player" or the "second player." The first player always activates first, and selects one of the second players objectives to be the objective for the game.
The "first player" is the same thing as the player with initiative:

The person with fewer fleet points (or in the case of tied fleet points, the winner of a coin toss) gets to decide who will be the first player:

