As Bloomer, I aim for 3' into the ground. Lay the hanging post on the ground, position the gate alongside it, and mark the post with:
1. Depth into the ground mark.
2. Position of hinge pins in relation to gate hangers.
3. Allow clearance of around 4 or 5 inches from bottom of gate to ground.
4. If using as a strainer, it'll need bracing. Also bang in a few 6" nails a couple of inches staggered about into the area of the post designated to be submerged in concrete. This will 'lock' the post and prevent turning when the wire is tensioned.
If you're using metal gate posts, then obviously only 1,2, and 3 above apply.