Baptists are traced at least back to the 1600s. Anabaptists lived during Luther's time though their theology varied. Mennonites have a strong kinship with Baptists as well. Methodism was an offshoot of anglicanism in the 1700s through the Wesleys. Likely a strong puritan kinship there as well. Beyond that, Protestant beliefs can be seen stretching throughout history. While Catholicism was by far the majority belief from the 300s forward, they weren't the only game in town. Unfortunately, they had a tendency to burn other people's writings so some of the beliefs of other groups such as the Petrobrussians, Waldensians, Lombards, etc., are lost. We may have some pronouncement against them by the Catholic church. But, like Anabaptists, they may be far more diverse in actual belief system than current historical knowledge may allow.
There was also that little matter of the Eastern/Western church split that shows a state of fragmentation which continues to this day.
You are right. Anabaptists were persecuted by Lutherans and Catholics. But they did not make up the "mainstream" Reformed group. I am not sure how Baptists became so prominent in America, but in the historical sence, they were not among the major three.