Ideally, you would purge the keg before transfer if you have the means. If not, no worries. Transfer from fermenter to keg, place in the chest freezer at 40ºF, purge the headspace if you did not already purge the entire keg, then put on gas at serving pressure i.e ~12 psi. Then leave it to carbonate and condition. Drink when ready. That's it.
Carbonating at serving pressure is too low at room temperature, as the volumes of CO2 that will infuse into the beer are temperature-dependent given the same pressure. You would need 28 psi @ 65ºF to equal what 12 psi @ 40ºF would give you. Plus you'd miss out on the advantages of cold conditioning while carbonation was occurring.