3 Lights, One Switch, Power at 1st Light - HELP!
You'll need to run 12/3 to the switch anyway to conform with current Codes, but the 12/2 between the lights is OK
The issue with the diagram you posted is that it predates the 2011 NEC's amendments in 404.2(C) to require neutrals at light switch locations so that you can install a smart-switch down the road without having to make a fuss over things.  This means that instead of using a 12/2 from the light to the switch, you'll have to use a 12/3, with the white in the 12/3 used to provide neutral at the switch location.
The good news about that, though, is it means that putting the receptacle at the switch location will Just Work, as all the correct wires for it will be there anyway.  Once you have the switch and receptacle working, with switched-hot available at the first light fixture, then the onwards cable gets connected to switched-hot and neutral, with each subsequent light fixture connected between black (switched-hot) and white (neutral) of the onwards wiring.
Of course, this assumes that you're routing the switch loop from the first light fixture in the chain (where power comes in at).  If you want to place the switch loop at the last light fixture in the chain, then you're stuck replacing all the 12/2 between the light fixtures with 12/3, as you'll need to bring always-hot all the way out to the switch, then bring switched-hot all the way back to the first light, while providing neutral at every point in the chain as well.