I've set up an off grid solar system out of necessity. Used to be an electrician so I know a good bit (but not everything by any means). What are your questions I can maybe point you in the right direction.

Based on your initial question, it depends on local zoning. You can likely legally grid tie a set up and have a battery backup. I think if you want to be legal I'd go that route.

If you want I think you could set up a completely separate system in a more sneaky fashion that is completely isolated from the grid / your existing house circuitry. But when grid tying (including into your house circuitry) you have to be pretty safe because that power can go upstream and feed the grid or the house when workers think the power is off, which is obviously very dangerous and could get you in a lot of trouble if it went wrong.

Why would you pass up on the free money of selling the power? You're probably looking for a hybrid system if you just want to keep the lights on during a service outage. Or I guess you can just build an off grid system and wire it to a generator transfer switch if you want to power your house circuits but only during an outage.

Most half decent solar installers can help either way.

I bet the Solarpunk and homesteading / permaculture communities might have some ideas on this!

Best ask in a more specialized forum. Personally I rent so I have to take what I'm given.