There's 3 ways to run solar.
Grid tied, grid backed and off grid.
I live on a farm and am off grid. The solar inverter is my "utility". After the inverter I have my main breaker. The inverter makes 5 kW max at 230 volts, so my fuse is 5000/230 = 20 amps.
I'm outside the US, regulation is a suggestion here everyone ignores. So many many houses have solar panels here to offset grid costs ($0.60 per kWh).
The main way we do it is make it grid backed. This means the inverter creates power that is in no way mixed with grid power. It forms a microgrid within the home. All ac's are connected to this. This can be done in the electrical panel as its just rerouting wires to fuses.
So then you have your 20A fuse behind the inverter, and smaller fuses (which you should already have) to your house loads. Btw you guys run 110v so your fuses are probably double the rating of ours.
When you do grid backed a battery is nice, since it helps prevent using the grid when a cloud passes by, it forms a bit of buffer. A 5kWh battery already helps. At night the grid powers the loads.
Grid-tied is the one nobody here uses, so you can feed back to the grid. This involves complicated electrical stuff so you don't electrocute the line workers. Plus it gets complicated with split phases and such.
Not to mention utilities pay less than what they ask you for the same kWh.
In the case of balcony solar you can feed the inverter utility power and connect your AC to the inverter. It uses solar power first and takes the needed diff from utility.