I nearly 100% of the time raise the main first and typically do it while on our mooring. The few times that I don't raise it on the mooring is if there is 15 to 20 kt winds as we need to go in a certain direction get into the main channel and sometimes the main and the motor be working against each other . Not that the we can't dump wind from the main, but it just makes steering more difficult especially as we leave the mooring. In these instances, we wait until more open water to raise the main.
The jib/genoa is raised second. Sometimes we do it running or reaching, but usually not when close hauled unless very light (6 kt or less) winds.
As far as which sail to drop first, usually it is the headsail, but I have dropped the main first and rolled in the head sail to a very small area and used it to sail onto a mooring more effectively in a breeze with two people. As we approach the mooring we come in on a close reach or "close haul" at about 3 kt boat speed at the right moment, spin the boat, furl the remaining head sail exposed while gliding into the mooring. We try to time it to "overshoot" the mooring by about the 3 ft which allows me time to pick up the pennants while the are slack and get them on before the boat gets blown backwards by the wind. My wife hates when we do this (no motor), but she knows it is a critical skill to have.
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