Bts,
Your thread title says captain to captain so I assume that's the plan about which you're asking. Unless you have previous FAA Part 121 experience, you'd be unable to slide in here as a captain straight away...regardless of your experience. It's a government thing.
Read this FAR with attention to section (a)(3):
https://www.law.cornell.edu/cfr/text/14/121.436#
You've got the legal ability to work solved via your dad's citizenship.
As far as T & C, only you can answer that. There are some outfits with fabulous deals...and probably more with terrible deals.
With your experience and a green card you might just be legacy airline bait once you've got an FAA ATP (the seniority structure just is what it is). Do you have a 4-year college degree ?