Did they have to have reasonable money to make the voyage? Or were they generally poor and trying to escape that?
(This is an English perspective on the question)
I can't give you an answer about average wealth and the cost of the crossing and such, hopefully someone else can answer the question more specifically - but I can say a little bit about what sort of people they likely were.
In the sense of being a 'Puritan', nonconformist Christians in England were usually (though there are always dangers in such generalisations) fairly comfortable by 16th/17th Century standards.
Your average Puritan (many historians don't like this word) might have been a relatively well-off smallholding farmer, or often they were merchants and traders. There's a certain self-selection to being a Puritan in that you would have been literate - nonconformist Christianity had a heavy emphasis on Bible study and a more 'revelational' with God rather than believing what you were told by the local priest and bishop. thus you were most likely not on the very bottom rung of society.
They probably would have had the money to provide for the voyage; your average poverty-stricken peasant would not have the money, knowledge, connections or inclination to make a long and dangerous journey to a place where they might well not survive.
I recently read a great book about a family who are the epitome of the sort of Englishmen who had strong links to the Plymouth and Massachusetts Bay Colonies, its called the Rainborowes by Adrian Tinniswood.
http://www.amazon.co.uk/The-Rainborowes-Adrian-Tinniswood/dp/0099555751/ref=tmm_pap_title_0
Thomas Rainsborough/ Rainborowe is famous for students of the English Civil War as a radical captain in Cromwell's New Model Army. When the Army met at Putney Church in 1647 to decide whether to do a deal with the King and discuss demands, he said this:
"I think that the poorest he that is in England hath a life to live, as the greatest he; and therefore truly, Sir, I think it's clear, that every man that is to live under a government ought first by his own consent to put himself under that government; and I do think that the poorest man in England is not bound in a strict sense to that government that he hath not had a voice to put himself under"
I think old-fashioned American histories go a bit too far in tracing America's origins to this lot, but you can see why people are attracted to the Puritans.
(Sorry went a bit off topic, but they were a very interesting group of people)