Just watched The New World and was wondering how life was aboard those ships that charted for new lands. I want to do extensive research for a project
You need to pick up a copy of Pablo E Perez-Mallaina's Spain's Men of the Sea: Daily Life on the Indies Fleets in the Sixteenth Century. Granted, its a bit earlier than you want, but it has the most well researched material on naval life for the Early Modern period.
For the specific period you're asking about, this is a good resource: http://www.boydellandbrewer.com/store/viewItem.asp?idProduct=13786
Also, N.A.M. Rodger's "The Safeguard of the Sea" is a good general overview, though its coverage of the 16th century only amounts to ~100 or so pages of the book: http://books.google.com/books/about/The_Safeguard_of_the_Sea.html?id=bYO2hAe1Db8C