You need a battery for the initial surge when using the inverter, and to keep the amps up when a cloud or person walking by temp drops the solar output, any normal grp 24 or 27 will do. With full sunlight on the panels the solar output will run the inverter. From my experience, on a very hot summer day (100+) with a constant heavy load for hours I can get a consistent 650 watts out of the 915 watt total system using a prowatt 1000 inverter; the heat on the panels and the inverter getting hot really reduces efficiency. On very cold sunny days it can get up to 960 watts of output.
My personal opinion is the Victron controllers (smart controllers with built in Bluetooth, not the older non Bluetooth models) are far more advanced than any other manufacturers controller, small in size, stay cool, and their prices are good and I have had great success with their reliability (I own 4 of them). I happen to have a 150/85 hooked up to 3x305 watt panels right now.