That depends on what options are available to you for residential solar installation. Installing solar panels + micro-inverters is very cheap in cost of parts, but possibly expensive in labor. It will easily pay off your grid interconnect fee every month once you hit break-even from operating for a few years. Financing vs cash, cost of installation, tax credits, are the biggest factors in how quickly it becomes profitable. If you are extremely handy you can DIY most of it as a homeowner (depending on local/state laws) which cuts costs significantly.
You can do a whole home backup + solar panel input (aka ESS+PV) but it's much more expensive in parts and installation and is more complex. If you don't add grid interconnect it can be much cheaper as you can use "off-grid" parts (grid interconnect requires more expensive parts certified for certain standards).
But some jurisdictions may not allow cheaper "off-grid" parts/systems to be connected to the grid, even downstream. So an alternative would be to install a transfer switch, where you manually switch from the grid to off-grid. But then you literally have to choose whether you use the ESS+PV or the grid at any given time and manually throw a switch (you can't use grid to charge your system). And yes you can set this up for only specific circuits/appliances. Again it depends on your state and local laws.
AI can do most of the research for you. Keep a Git repo and add documentation and details to it over time, and you can build up an analysis of what works for you based on all available options, price comparisons, energy requirements, and local/state laws. It is unfortunately quite complicated because there are many options but not all will apply to your location. And before you do any of this, do a solar site survey to see if you can even reliably generate enough power from the sun!