It's good to have you looking at actual Scripture in actual context. You are free to keep it as simple as you like. I'll take it word by word and define every word and grammatical construction in places and follow the context from phrase to phrase with all the grammatical markers. If we end up with the same meaning, that's a good thing.
For starters, I won't rely on the NIV. and I'll probably end up taking issue with it quite a bit. Secondly, since you're touching on it and seeing it in focus, the 3 phases of salvation concept is very often in view when "salvation is mentioned and contextual work may require us to determine what phases(s) are being discussed, So, what do you see as the main focus of salvation here, if there is one - #1, 2, or 3, or all or ?? or is it important (if it works for you, #1-3 is easier for me than the common Just., Sanct., Glor., which I don't care for because it's not really accurate)? You seem to be saying #1 is not in view. I'm not prepared to agree for a few reasons, but they're not that important at the moment, and I can flow with you for now. There are a few nuances I'm still looking at.
FWIW, looking at the options to translate the language elaborating a bit on the words, at this time I'd say: [God's} Gospel [concerning God's Son Jesus Christ...] is God's power for the purpose of salvation for the benefit of all [men] who believe [it/Him].
Since "salvation" can carry a nuance as a verbal noun (salvation <> saving) that language could be considered if useful for thinking and interpreting, to say "...God's power for the purpose of saving all [men] who believe it (and thus believe Him)."
From there, "from first to last" is interpretive. There are some other ways to interpret it that don't take us so directly into the 3 phases, and I have some thoughts I've carried for some time re: what Hosea is saying and how it may well be coloring Paul's use a bit differently than translated and then interpreted.
All of this really boils down to what point Paul is making before he gets into the part about Knowing & Understanding God. He's dealing with the revealing of God's wrath vs. God's righteousness. And there is a likelihood that righteousness and salvation are parallels.
FWIW, we may not be too far apart on 1:16 and I'll leave that for you to decide. Here's my take for now: The context is mainly dealing with phase 2, that will have an effect on phase 2 and 3, but does not exclude phase 1 mainly because what God is doing in this includes bringing men into phase 1 so more are involved in phase 2, affecting 2-3, and the circle or increasing upward spiral continues.
For you, I think you're going to have to consider what the power of the Gospel is in drawing more men to Jesus Christ as more and more men are revealing God's righteousness which in reality is what God's Gospel does. And if God's righteousness and God's salvation are indeed parallel here (as they are in places in OC Scripture as I recall) then what is the power of more and more men revealing God's righteousness / God's salvation comprehensively by faith?
Simple works at times. What Paul is saying is not simple until he's more fully understood, Peter.
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