If you're going with wood post I'd find hedge (osage orange). I've seen them up to 18-20" dia. used for gates and where fence makes a turn without a corner post. Out last steel, yet it's wood!!
If your really ant to secure a post for a gate, once the post is in the hole dig a trench (that would be perpendicular to the closed gate) on the gate side of the post. Lay a post horizontal in the trench right up against the upright post. That anchors the post from leaning over time.
If your really ant to secure a post for a gate, once the post is in the hole dig a trench (that would be perpendicular to the closed gate) on the gate side of the post. Lay a post horizontal in the trench right up against the upright post. That anchors the post from leaning over time.