If Watts = Volts x Amps (and they do).
3000= 27 x X so 3000/27=111 so your 24V wiring will need to carry 111 amps at 3000 watts. Your 60 amp breaker won't work out.
You likely will spike your power when pumps or motors start as well.
I would use a 150Amp fuse, 150A wire, 150A breaker.
I prefer the type T marine fuses for robust reliability. #2 welding cable would be my choice as it is rated for high capacity and is pliable making it easiest to work with.
#2 welding cable - ebay
Fuse
Please do not connect the batteries like that.
Connect them in series - like this:
24vdc + red wire-----POS Battery NEG------POS Battery NEG-----black wire 24vdc -
Probably going to want disconnects or breakers on the 230 in and 230 outs.
Likely collect 4kwh - hope that is about what you expected.
Battery monitor will likely be built into the inverter.
It takes power to run the inverter. My big inverter uses 250W (6kwh), my smaller inverter uses 100w (2.4kwh) / day. This is being consumed when the inverter is powered on, there are also efficiency losses in the charging, discharging and inverting processes.
Friend I have compiled much of my experience into this video, you might find some value in it. GOOD LUCK, ALL THE BEST!!!
Solar Power for the Full Size Home