To me these
are the key verses of Romans that are particularized at least in the first 11
"For I am not ashamed"--honor/shame language we often pass over but that meant something in the first century. Hays thinks Paul may be echoing some OT passage like Isaiah 50:7-8 where the prophet says "I know that I shall not be ashamed because the one who justifies me is near" (Echoes)
"of the gospel"--the good news, as Wright points out, is the good news about what God has been doing for Israel and the world through Christ (What Saint Paul Really Said).
"for it is the power of God to salvation"--Salvation for Paul primarily refers to something that will happen most literally on the Day of Judgment when we escape God's wrath revealed against all ungodliness and unrighteousness of humanity (cf. Rom. 5:9)
"to everyone who has faith, the Jew first and also to the Greek"--We remember that the verb to believe, (pisteuo), is simply the verb form of "faith," (pistis). The Jew first and also to the Greek reminds us that Romans is all about Paul's defense of God justifying the Gentiles by faith. His basic argument is, that's how Jews are justified too.
Therefore, Romans 9-11, which talk about the ultimate salvation of the Jews vis-a-vis the Gentiles, are not a diversion but the very climax of the first part of the letter and the playing out of this principle.
"For in it the righteousness of God is revealed"--the overwhelming majority of Romans scholars now see the righteousness of God in reference to God's righteousness in this phrase, although some connect it more to God's covenant faithfulness to Israel (Wright, Hays) and others to God's universal action to justify the world (Kaesemann, dead now about seven years or so). I've mentioned at least one Psalm Hays thinks Paul may have in mind. The second half of Isaiah is also replete with parallels between God's righteousness and His salvation (e.g., 42:6-7; 46:13; 51:6; 56:1; 59:16; etc...).
This doesn't mean that righteousness for humans isn't a part of Paul's thought or even less does it mean that righteousness for humans isn't a part of the Christian theological equation. Here we are merely asking what Paul is likely to have meant by this phrase, and here the case seems fairly well stacked toward God's righteousness.
"out of faith into faith"--difficult phrase. There seem to be two main interpretations: 1) that it is intensive a la NIV: "by faith from first to last"; 2) that there is some sort of progression here, from x's faith leading to y's faith. The majority position here is "starting from God's faithfulness and leading to our response in faith" (Dunn, Hays, etc...). Here we reference the first part of Romans 3 and the faithfulness of God mentioned there (e.g., 3:3), along with the sense that the righteousness of God is related to His faithfulness.
Some, however, (e.g., Douglas Campbell) would argue that it is "from Christ's faithfulness to our faith response." Possible, but I'll leave it at that.
"As it is written, 'The one who is righteous on the basis of faith will live.'"--Habakkuk 2:4. Hays thinks Paul may have understood this as a prophecy about the Messiah: "The Righteous One will be resurrected on the basis of His faithfulness." It just doesn't seem to me that we have enough evidence to conclude this idea with any certainty at all, although it is possible. I personally take the "on the basis of faith" passages more with Dunn in Romans and Galatians as references to the basis by which humans are justified before God.