That's going to be a little different than a small homebrew on a pushup pole. You'll need to concrete in a base and erect a tower for anything that big.15 to 20 gain would be nice but then I'm not certain how many FT**2 I can support on top of the house.
I'm not concerned with rejecting any noise from the w-wsw.
Over earth (ground gain) the dipole will show ~7dBi, and the moxon ~10dBi. To get into 15-20dBi territory you are talking at least a 5 element yagi.