For sizing the wires between batteries and between batteries/inverter....how big is your inverter in Watts?
Say it's 1,000 Watts. That's 1,000 W / 12 V = 83.3 A max discharge current from the battery. Using a chart like this one
and assuming your connecting wires are less than 10 ft (keeping them short is good), you should use 4 AWG wire.
Of course, adjust the numbers if you have a different sized inverter.