I did New Mexico. Won't say it's the best, but it had things I wanted. South Dakota is a good choice for domicile because it's easy and cheap.
The easy way around the address situation for everything else is ta use a private mailbox service, like a UPS Store. That gives you a street address, and you write down the mailbox number as Ste, Apt, or just #. I even use mine for car insurance.
How's the health insurance there? I have a cheap plan from NY but I'm not sure it even works outside the state.
Can't really compare. I got the extended Medicaid. It's real good.
The NY medical insurance probably doesn't cover much here besides emergency care. When I was traveling more widely with a Bronze plan from Texas, all it got me was price-negotiated meds at Walmart and other chains out of state, and emergency care out of state. I had to haul all the way back to Texas for doctor appointments. The New Mexico insurance has the same deal.