Hybrid inverters do everything automatically.
Solar if available, then battery, then grid. They will also top up from the grid or battery if your solar isn't producing enough.
I've the cheapest 5kw hybrid I could find at 12kbht, works perfectly. Supplies 80% of my needs 24/7, but I did cheat by keeping my cooker, Aircon and 4kw shower heaters on grid supply.