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.