The statement that the faith of the Romans “is being reported all over the world” (Romans 1:8) is evidence that the Christian community of Rome had grown to some size. Raymond E.Brown says in An Introduction to the New Testament, page 561, that Paul’s letter implies that the community had been in existence for a long time, since he had been wishing “for many years” to visit (Romans 15:23). This also tells us that Paul had never visited Rome at the time he wrote this letter.
To me, the Epistle to the Romans is a job application, albeit an unsolicited one. Paul spends the first chapter winning the trust of the Romans, assuring them that he would fit into their group, and closes by assuring them that he has no intention of stepping on toes and will not outstay his welcome, because he plans to proceed to Spain after a short stay in Rome (15:24,28). He provides a detailed resume by laying out much of what we know about his theology.
As with his other epistles, Paul’s chief message is utter opposition to adopting Jewish law, especially on circumcision, and he spends a large part of the epistle making his case. This points to Paul's belief that a large proportion of the Christians in Rome were gentiles, who were being pressured to undergo circumcision. But they were not all gentiles. In Romans 2:12-15, Paul is careful to gain the support of Rome's Jewish Christians as well, saying that people will be judged according to what they do – Jews according to the Law, Gentiles according to nature, which is based on the Law.
Because there was as yet no leader of the church in Rome, Paul's letter was written to the congregation as a whole (Romans 1:7: "to all the beloved of God in Rome, called to be holy..."). This no doubt included freemen and slaves, gentiles and Jews.