Did NT churches immerse? Generally agreed, even by the Catholic Encyclopedia.
Did NT churches immerse believers? Generally agreed, though some Presbyterians are "doubters."
Did NT churches demand faith before immersion? Generally agreed, with exception as noted.
Did NT churches teach "security of the believer," based in salvation by grace through a repentant faith? Not so generally agreed, but widely enough accepted to make a strong case. (Here the Presybterians are our allies!)
Did NT churches operate "independently," yet with links of doctrine and spiritual accord, without any formal ecclesiastical organization "over" them? See Mosheim's Church History (Lutheran) for thorough documentation of this point.
Have there been autonomous, self-governing (under Christ)local, visible congregations of immersed believers, however few, however scattered, however differing among themselves in incidentals, in every age of Christian history? Most historians would agree, even while many of them spend lots of time pointing out the various differences among such churches, and between them and our churches.
Were such congregations persecuted by the state religion in the "Dark Ages"? Generally agreed.
To the extent that we have a succession (and I'm with Mark O. on JTChristian's superb work, which I've used in teaching Baptist history for years), it is of necessity among the persecuted, despised congregations of immersed believers (and maybe a few "sprinkling Anabaptists" in the 1500's, though many of them did immerse). Our succession as promised by Jesus in Mt. 16:18 and 28:18-20, and by the Holy Spirit in Eph. 3:20-21, cannot be among those persecuting "official" religious groups living in an incestuous relationship with pagan government after Constantine. Whether or not we can trace it, by faith we affirm that Jesus made no mistake when He promised it. The persecutors taught "salvation by works," starting with infant "baptism" and leading to "sacraments"
of various sorts, moving even from immersion to sprinkling at the Council of Ravenna, 13th cent.
Whether all the persecuted groups were "alike" is irrelevant; among them we find some like the NT, and to the extent that we are like the NT doctrine we are NT churches. The word "Baptist" came into general use in the early 17th cent., but as Mark has pointed out, it is largely interchangable with "Anabaptist," and the name is not the primary issue; the doctrine comes first.
Ours is based squarely in the NT, as we have been led (we believe by the Spirit of God) to believe and begin to understand it.
Wishing you all His best - Charles - Ro. 8:28