Hi,
#4 wire is not good for 150 amps, maybe 100 amps, but not much more.
#2 wire is better at 150 amps, #0 is even better, depending on the length and the time you might spend at over 1,000 watts output you might consider the larger wire.
That said, if you don't expect to have more than 1,000 watts going through the inverter, 100 amp fuse and #4 wire will be OK, if the length is under say 10'.
If the main wire is #2, then a 150 amp fuse will be fine.
I have had a "E-Meter" for about 10 years, and still enjoy it. It was built before the Trimetric. They are very accurate, and a great tool to know when to run the generator or leave it up to the solar system to refill the batteries. I would run the generator for a hour or so in the mornings if I had used more than 120 AH the night before, it would charge at about 45 amps for the first hour, then slow quite a bit to about 30 amps or less, so I would let my 400W solar system finish filling the battery bank, I had 440 AH at 12 volts in 4 golf cart batteries.
Fred.