I have a great deal of information concerning Maryn Adriaenszen. He and his wife have been subjects of my research for many years. I will give you a brief of what I know, then tell me what details you would want to see.
Based on the various records in New Amsterdam, Maryn Adriaenszen was from Veere. He served as Boatswain under Captain Claes Gerritssen Compaen, probably from 1621-1627. He married Lysbet Thyssen around 1628 and may have been in New Amsterdam as early as 1630 where an unnamed son was born. Maryn returned to the Netherlands where he entered into the contract with Patroon Killaen van Rensselear and returned to New Amsterdam in 1631 as you have noted. His daughter Brechje Maryns was born around 1631, after they arrived. Maryn removed with his family from Fort Orange (Albany) to Fort Amsterdam (NYC) by 1639. He was an influential individual, but in 1643 led an attack on a group of Indian, which resulted in slaughter. Maryn was being called "murderer" and Director Kieft was trying to publically shift the political responsibility onto Maryn. In a fit of anger, Maryn attacked the Director, for which he was arrested and sent to the Netherlands for trial - he was too popular amongst the locals in New Amsterdam for him to be tried there. He had returned to New Amsterdam by 1647 when he received a patent for land on the New Jersey side of the Hudson. Maryn had died by 1654 when his widow remarried to Geerlif Michielssen. They apparently had a son named Tys Marynsz, who was born before 1637. The unnamed son and Tys do not appear to have reached maturity. All descendants of Maryn Adriaenszen are from his daughter Brechje Maryns who married first Claes Cornelissen van Voorhout and second to Jan Tyssz Goes.
There are not many details on Lysbet Tyssen. She had a brother named Pieter who resided in Alkmaar in 1649, whom she had sent a Power of Attorney to for the collection of monies due her from the estate of another unnamed brother and sister who were deceased. I have quite a few records for her in New Amsterdam as well. She died around 1680, her only surviving child being Brechje Maryns.