Concerning the continuity between circumcision and baptism: although both signs serve as an initiatory rite, there is a core difference in their significance. Circumcision had more than a spiritual purpose in the Abrahamic covenant.  Its primary purpose was to “mark out a physical seed in preparation for the coming of the Messiah” (155). Stephen Wellum aptly summarizes:

In this new era, a new covenantal sign, baptism, has been established to testify to the gospel and to identify one as having become the spiritual seed of Abraham, through faith in Messiah Jesus. But unlike circumcision, baptism is not a sign of physical descent, nor is it a sign that anticipates gospel realities. Rather it is a sign that signifies a believer’s union with Christ and all the benefits that are entailed by that union (157).

For a wonderful essay, see Stephen J. Wellum, “Baptism and the Relationship Between the Covenants,” Believer’s Baptism: Sign of the New Covenant in Christ, ed. Thomas R. Schreiner and Shawn D. Wright, NAC Studies in Bible & Theology, ed. E. Ray Clendenen. (Nashville: B&H Academic, 2006), 97-161.