Battery configuration for inverter?
Three car batteries (or other 12v 50Ah batteries) in series would make an ideal battery to supply a 36v input inverter. 

Three 12v batteries of 50Ah store 50% more energy (run time into the same end load) than a single 12v battery of 100Ah.

An inverter you have will cost you rather less than one you have to buy.

A 12v input inverter will not be more efficient than a 36v input inverter, and will need thicker wires to supply it.