I second /u/Bodark43's recommendation of the van der Donck book as a primary source. It gives a valuable early description of New Amsterdam.

You can find further early descriptions of New Amsterdam in Narratives of New Netherland 1609-1664 edited by J. Franklin Jameson, which collects together early narratives from various sources.

Other primary sources you may want to consult are the translations by Charles Gehring of original Dutch manuscripts provided for free by the New Netherland Institute. These are the most recent translations of these manuscripts, and are generally considered the most authoritative (though they are not yet entirely complete--allegedly, the rest are still due to be published at some point in the future).

An earlier source of primary documents is the Documentary History of the State of New York series by Edmund Bailey O'Callaghan (a.k.a. E.B. O'Callaghan). He was the state historian of New York in the mid-19th Century and was the first one to translate the surviving Dutch manuscripts en masse into English. He also wrote a two part history of The History of New Netherland which may also be of use.

For secondary sources, I would recommend The Island At The Center of the World by Russell Shorto as a good starting place. It's well researched and is more readable than most other histories of the Dutch period of New York, and covers all the major events while also adding some new insights here and there not always found elsewhere.

Another good secondary source is The Colony of New Netherland: A Dutch Settlement in Seventeenth Century America by Jacob Jaaps. It covers the same ground as Shorto's book, so if you read both, you're going to get descriptions of many of the same events, but it's always good to have multiple perspectives.

A short blurb to give you a general answer to your questions: Most of the people who came over during the Dutch period were coming over for financial gain. The colony was initially owned by the Dutch West India Company, whose primary goal was to make money for their shareholders. As such, they hired people to administer the colony, and also tried to convince potential colonists to make the trek over. That didn't always go how the company wished, but that was the motivation of most people who came.

Some groups also came for the religious tolerance that the colony promised. The earliest permanent settlers are thought to have come from Wallonia, which is now the French-speaking part of Belgium. They were Huguenots, i.e. Protestants escaping their French homeland at a time when Catholic rule in France was strict. Other early settlers included the first group of Jewish refugees in North America, who came to New Amsterdam in 1655. English Quakers also came, founding one of the six towns that would eventually comprise the borough of Brooklyn.

Those who were more motivated by the monetary aspect mostly came from the Netherlands and Scandinavia, but people from all over Europe came during the Dutch period, mostly Protestants. There were some Catholics who came over, but most of that happened much later, long after the Dutch period.

Anyway, this is covered in much more detail in the Shorto and Jaaps books, so I would start with one of those to get a basic understanding of the period and go from there. Good luck!

I would suggest Bernard Bailyn's The Barbarous Years: The Peopling of North America for a start. I think that the very small, fragile European colonies of the time are best understood in groups, because they affected each other ( the English and Swedes are an important part of the story of New Amsterdam) and each of their interactions with the Native American tribes tended to have repercussions for the rest.

For a primary source, Adriaen van der Donk's Description of New Netherland has been translated into English, and is valuable. It is remarkably sympathetic to Native Americans and says a good bit about the area. There are older translations of it out there that are being offered by print-on-demand companies. I think the newer Goedhuys translation is more useful.

Thanks to both of you. This is tremendously helpful.