If you will have a regular propane/elec fridge, then it should be an autoselect as to power--if plugged in, will operate on electricity and if not plugged in, should automatically shift to propane. Assuming that you have propane and tanks are open.
When driving to campground, fridge should be running on propane, and will change to electricity when you plug the trailer in at the campground. Haven't seen a manual select in a long time, nor a 3-way fridge.
The fridge will ALWAYS need good 12-volt power to operate properly; if you let the battery(s) run down, the fridge won't operate.
And, yes, pre-cool the fridge and have all food cold when you put it in. Should take anywhere from 8-12 hours to cool, perhaps longer if outside temps are high.
'05 36TK3 Mobile Suites
'10 F450 new to me
'09 F450 Lariat 4x4--died