I also see I am a little shaky on the whole Anglican/Puritan/Baptist question, who is what.
An Anglican is a member of the Church of England or a branch of that church, such as the Episcopal Church in the US or the Anglican Church of Canada. Since it was a national church meant to encompass the vast majority of people, the Church of England has for most of its history adopted a big tent philosophy–with high church/low church and Calvinist/Arminian factions.
Arminians are Protestants who believe in free will and conditional predestination, which often makes Calvinists accuse us of being semi-Pelagians, humanistic, or more Catholic than Protestant. Evangelical Anglicans can be either Calvinist or Arminian and many denominations that split from Anglicanism (Methodism, Pentecostalism) are Arminian.
Puritanism was a 16th and 17th century Calvinist movement within the Church of England that wanted to purify the English Church of all remaining Catholic practices (liturgy, episcopacy, etc.). During the English Civil War, Puritans ascended to power and attempted to transform the Church of England into a presbyterian (rather than an episcopal) church–basically along the lines of the presbyterian Church of Scotland. The English Puritans wrote the Westminster Confession–which was adopted by the Church of Scotland while being rejected by the English Church once the monarchy was restored. In England, Puritans were eventually forced out of the national church and became Congregationalists (named after their preferred church polity) and Presbyterians.
In America, Puritans came to New England and founded Massachusetts and neighboring colonies on their religious principles. They evolved into the Congregational churches (many now members of the United Church of Christ).
Baptists originated in England as Separatists–people who wanted to separate from (rather than purify) the Church of England. Unlike Puritans (who still practiced infant baptism), baptists adopted adult baptism. Like Puritans, however, Baptists favored congregational church government.