Basic steps of moving to Brazil.

Hi!
I did exactly what you're planning in 2017.  It's easy, as long as you stay organized.  Keep in mind that, technically, until your application for permanent residency has been accepted, it's your wife who will be making the requests for both of you (you'll even see that referenced in the Polícia Federal material below), so you do this as a team.

Step 1 -- Register your US marriage with the Brazilian Consulate General in Atlanta, assuming that you're currently living in Georgia.  This is a good one to get out of the way as soon as you can.   The instructions for doing this appear on the Consulate's Portuguese pages only, here:

http://atlanta.itamaraty.gov.br/pt-br/r … amento.xml

The Consulate General, unlike the Polícia Federal when you get to Brazil, will accept documents in English, no translation needed.  They will issue you a Certidão de Casamento; it's a good idea to get a "2a via", a duplicate original, at the same time, When you get to Brazil, you will present the Certidão from the Consulate  to the Cartório do 1o Ofício in your wife's hometown,  A week or two later, you'll go back to the Cartório to pick up your "Traslado de Casamento", the document that confirms your marriage's legal effect in Brazil. 

Step 2:  Request your VITEM XI  visa.  You don't have to do this until you know your departure date.  When you register your marriage, you can ask the Consulate when the best time to apply will be.  The VITEM XI is the Temporary Visa for Family Reunion,    One of the requirements is to have completed the registration of your marriage, above.  The other requirements appear here:

http://atlanta.itamaraty.gov.br/en-us/vitem_xi.xml

Step 3:  Register with the Polícia Federal as soon as practical after you arrive in Brazil, and request permanent residency.  The requirements appear here:

http://www.pf.gov.br/servicos-pf/imigra … o-familiar

This is where your planning comes in.  Many of the required documents will require apostilles, from one of the United States, from the US Government (for Federal documents), and perhaps, from the UK.  You want to have these in hand when you get off the plane in Brazil.
Note that you will be required to provide a FBI Background Check.  On the day you file your request for permanent residency, your Background Check must be less than 90 days old.  So, you'll want to use a FBI Approved Channeller, and time this document to arrive early enough to get an apostille from the US State Department, but late enough to be fresh when you get to Brazil.
All English language documents submitted to the Polícia Federal require a Sworn Translation, prepared by a Sworn Translator authorized by the Junta Comercial of a Brazilian state.  You can arrange for that once you arrive; don't waste money on informal translations, because they won't be accepted.
Once your application has been accepted, you will receive a Protocolo indicating that fact.  In between one and three months, you'll be called back to the Polícia Federal to pick up your CRNM, Carteira do Registro Nacional Migratório, which will be your national ID card.

Step 4:  Register with SUS.  This is easy, especially after you have your Protocolo, although you really don't even need that.  Just go into any facility of the State Health Department, like a community clinic, and ask where you can register.  Very often, it will probably be in that very place; if not, it won't be too far.  You'll walk in, register, and walk out with your SUS card.

Any other questions, feel free to ask.  Enjoy the adventure!