Car Insurance Costs
Congrats on the move! Because car is priced at the zip code level and regulated at the state, you're going to want to update your car insurance to reflect that. Bear in mind, your premium will change as a result of your move.
You should use the address where you are currently living, especially if you don't know the address of the place where you are moving. The problem is, you will likely have to start a new policy once you move to Wyoming since each state has different insurance requirements. This also means that you will have to cancel your previous insurance policy and hope for a refund.
For the purpose of complying with your new apartment's landlord, it's best to change the address on your policy before you move in. This will satisfy the insurance requirement for your new place.
The state of Florida requires that you register a car within 10 days of starting a new job in the state or enrolling a child in school. Your insurance company doesn't care where the vehicle is registered because you have to get insurance before you can register it anyway, so that shouldn't be a problem.