You did not show in your pencil-drawn plan which side the gate hinge is on and which way the gate is intended to open. So here's something to think about.
* B
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* A
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(Apologies for ASCII diagram..)
If the hinge of the gate is meant to be at point "A", and it intended for the gate to open to the left in this diagram, double check the size of the hinge. If you go with a post that is square to the gate, you might find the gate does not open flush against the wall of your house due to the post blocking it from opening the whole way. In this case, you'd definitely want the post square with the house, not the gate.
Scenario: Post square to gate
Outcome: Gate does not open flush with wall of house
* B
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* A
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Compared to:
Scenario: Post square to house
Outcome: Gate does open flush with wall of house
* B
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* A
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(If the gate is hinging on point "A" and is meant to open to the right, double check once again that your choice of post orientation allows the gate to open flush against the house)