The way I was taught, which works well, is (on a warrior anyway) to start on the right hand side of the panel and work left so:
Circuit breakers,
Carb heat - hot (changes air source as well as warming the air)
Switches (batt/alt) - you never know,
Mixture fully rich
throttle check - appy full power, if no joy, close it (don't want engine suddenly coming back to life just as you're flaring for your landing)
Mags - check each one, then back on both (DON'T do this during a PFL as I nearly did once - slap from the instructor there

)
Fuel Guages - check contents.
Fuel pump on
Change tank.
If it all goes to poo, then make your mayday call, and prepare for landing with
F - fuel - pump off, valve closed
I - Ignition - mixture cut off, mags off
S - switches off (you would have to leave BATT on on a C172 so you can lower the flaps).
H - hatches and harnesses
Obviously most of this is touch drill during a proper PFL 'cos you wouldn't want to make it a real one...