For the kind of power you want, I would recommend 2x SMA Sunny Island inverters.. They are heavy duty and will start an air conditioner without a problem.. They can also be stacked so you can add more later if you want. As for the battery size, that would depend on what kind of battery and how secure you want to be with energy storage... for how long you want to be able to run without sunshine.
If you go with lead acid batteries, you need a lot of solar array power because lead acid bats die quick if you don't keep them charged up every day.
With a lithium battery, it doesn't mind being in a partial state of charge.
I would also recommend a setup that allows you to plug in a generator to charge the batteries. A lot of these lower end inverters don't allow a generator hookup.
62kWh's daily is a lot of energy.. that's not a small system.
How much array you need will also depend on your location.