Wiring 101

Peter, your little trailer is fairly easy to wire.

If you want to go with 12 volt lighting, a converter will be needed. When on shore power, it powers all 12 volt items (lighting, cigar plug, water pump, etc) AC to DC.

The power distribution center is most likely a 110 breaker box combined with a converter and 12 volt fuse panel. They will charge your battery as well as convert 110 to 12 volt.

Converters do not convert DC to AC, that would be an inverter and much more than you need. Spendy as well.

Solar panels are separate and require a controller for the system. They can be incorporated into a converter system. Read the instructions on the distribution panel...

Because your trailer is a 76, it might have already had a converter/battery charger. Most trailers of that era did.

Please describe what was original and the sort of fixtures it had. Photos would help.