The short course:
They make adapters that allow you to plug either a 30 amp or a 50 amp rig into all of the following outlets
15/20 amp
30 amp
50 amp
Assorted Twist Lock outlets used on Generators.
Nothing wrong with a 2-step from 50-30-15
Recommendation ... For the first 3 on the list, carry the proper adapters for your rig so you can plug into any of the 3.. If you have a 30 amp rig and the park has a .. worn out, 30 amp socket, you can use the 50 that way.
IF you have a portable generator (PLEASE, an inverter type) get the proper adapter for it as well.
Now: Leaving it plugged in at home.
For short time (Setup (packing) and unset (Unpacking)) no problem. See Readdy Kilowatts Rules below.
For long term storage: Depends on your converter, post make and model of converter, NOTE on many trailers the converter is part of the power distribution panel.. ON this type of unit there will be a single door, often with a manufacturer's name on it like Parralex or WFFCO, and behind that door will be both 120 volt circuit breakers and 12 volt fuses.. The make and model are on the door in this case.
Good 3-stage converters you can leave it plugged in full time, IN fact, I did when I parked at home. Some, no longer made, I seriously recommend you do not do this..
Rules per Readdy Kilowatt.
On 15 amps.. Basically your converter and fridge.... YOU MIGHT get lucky and be able to heat water OR cool air OR microwave lunch if the batteries are full up.
On 20 amps.. same as above only delete the phrase Might get lucky" you can do these things IF THE BATTERIES are full up
30 amps,, Two of those thigns on the lucky list.. HOWEVER if you have two air conditioners.. Only one of those at a time.
50 amp: All you can eat (Everything on the list.
Televisions, epically modern LED/LCD jobs.. bascially do not count, they draw so little power the odds of them putting you into the click of darkness zone are next to zero. So watching TV or listening to radio, is an option under most all conditions.
Batteries, if hungry, can take up to six hours with a good converter, to charge, with a slower converter.. Delete bit about With full batteries since the state of charge won't matter.
My Converter draws about 10 amps if the batteries are low. That does NOT leave me enough for air conditioner, microwave or water heater on a 15 amp line, and in fact can trip a 20 with the fridge on AC. if you turn on one of those as my wife proved more than once.