@Alon A.
I would recommend the hub and spoke model. The hub is a LLC you own in a state like Wyoming or Delaware that has anonymity and the spokes are the ability for that LLC to own properties in different states. You can go a step further and put the property into a land trust.
For Example, you own ABC Investments LLC in Delaware. ABC Investments now owns 123 Main Street LLC in Florida and that LLC owns the property in a land trust. Land trusts don't violate the due on sale clause so how you finance the property will have no impact.
All your mail and any correspondence passes through your attorney. This strategy I have found to be the most effective for myself and the investors I help. This provides you 1) anonymity 2) a certain level of liability protection.
It is an expensive and complex asset protection and it could be overkill if you are just starting out, but something you want to look at later down the road. I am not an attorney and I recommend you always consult a Florida attorney before doing anything.