Below are excerpts from Dr. Helmut Koester's two-volume Introduction to the New Testament (Philadelphia: Fortress Press, 1982, Vol 2, pages 124-125, 138-139. A revised edition of these volumes, which is part of the Hermeneia series, has been available since 1995.)

Dr. Koester is a world renowned New Testament scholar. He has published extensively, has taken part in many archeological digs, and in 1998 retired as John H. Morrison Professor of New Testament Studies and Winn Professor of Ecclesiastical History at Harvard Divinity School.
 

Paul's judgment is quite different from his Jewish (Philo) and pagan (Musonius) philosophical contemporaries, especially since he argues without compromise for equal rights for women (e.g., 1 Cor 7:3-4). To this equal status of men and women corresponds the relativizing of the status of circumscised and uncircumcised people and of masters and slaves (1 Cor 7:17-24; cf. Gal 3:28)...

Whether women should preach and pray in church without a veil is not a question of emancipation, but a problem of the general custom of the church (1 Cor 11:2-16)...

The stay in Corinth during the winter of 55-56 marks the conclusion of Paul's missionary work in the region of the Aegean Sea. Further strengthening of the newly founded churches, preparation for his travel to the west, and organization of the delivery of the collection must have occupied Paul during this period.

Romans 16:1-23 witnesses to the first of these activities. It is a fragment of a letter that was likely written at that time and perhaps sent to Ephesus together with a copy of the Letter to the Romans (Romans 1-15). This hypothesis would also explain why this short letter to the "Ephesians" ended up in the later collection of the Pauline letters as part of the Letter to the Romans. That Romans as it is now extant was put together by a later editor is also evident from the doxology added at the end (Rom 16:25-27), which certainly is not Pauline. A number of manuscripts place the letter once circulated in different versions (the one used by Marcion seems to have ended with chapter 14!). The short letter of Romans 16 allows us an interesting glance into Paul's activities as an ecclesiastical politician. He did not devise church orders, but settled individual questions in the context of fortifying personal relationships. The first part of this letter is the oldest extant letter of recommendation for a Christian minister, namely, for the "missionary" and "congregational president" Phoebe from Cenchrea¹ (Rom 16:1-2; the tranditional translations of her titles as "deaconness" and "helper" cannot be justified on linguistic grounds). In the long list of greetings a woman is also named among the apostles (Junia, Rom 16:7; we cannot read instead the male name "Junias," because this name is  not attested anywhere else). Most of the persons named in this list are not simply personal friends of Paul in the church of Ephesus, but associates and co-workers. This is shown by the repeated references to their functions. The fact that such a large number of women appears in this list is clear and undeniable evidence for the unrestricted participation of women in the offices of the church in the Pauline congregations.

¹Cenchrea was a harbor town near Corinth, which was in the province of Achaia. The province immediately north of Achaia was Macedonia, which included Philippi. Everett Ferguson (Backgrounds of Early Christianity, Second Edition, Grand Rapids: Eerdmans, 1993, page 71) writes:
 

Macedonian women had greater independence and importance in public affairs. This coincides with the greater prominence that women held in the Macedonian churches (notice esp. the women associated with the Philippian church -- Acts 16:14-15; Phil. 4:2-3). Under the influence of the Macedonian princesses women came to have greater freedom in the Hellenistic Age.
 

And Paul wrote to the church in Philippi (Phi 4:2-3):
 

I urge Euodia and I urge Syntyche to be of the same mind in the Lord. Yes, and I ask you also, my loyal companion, help these women, for they have struggled beside me in the work of the gospel, together with Clement and the rest of my co-workers, whose names are in the book of life.