I would trace my non-immigrant lines first, so I could learn the ropes about U.S. vital records, censuses, city directories, etc, etc. Once I'm having really good success with American lines, then I'd tackle the immigrants.
Your public library has a lot of good books on basic genealogy. You may have a local adult school or genealogy society that offers classes for beginners too. I don't know what you mean that Tombo has a marriage index. Tombo is a portal to the CCA. The CCA has records to the districts, then islands, then councils, and then freguesias. Once you get down to the freguesia level, there are mostly birth, marriage, and death records. There are a few scatter records, such as legitimizations and indices, but these are incomplete. Ancestry and Family Search won't have anything on the Azores. Cheri Mello Listowner, Azores-Gen Researching: Vila Franca, Ponta Garca, Ribeira Quente, Ribeira das Tainhas, Achada -- For options, such as changing to List, Digest, Abridged, or No Mail (vacation) mode, log into your Google account and visit this group at http://groups.google.com/group/Azores. Click in the blue area on the right that says "Join this group" and it will take you to "Edit my membership." --- You received this message because you are subscribed to the Google Groups "Azores Genealogy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. Visit this group at http://groups.google.com/group/azores.

