Actually, there were two 1st NY regiments. Col. Jonathon Drake Stevenson's 1st NY regiment(originally the 7th NY) sailed to California and raised hell during the Gold Rush. The one that went down to Vera Cruz, under Colonel Ward Burnett (not Burrett). The 1st was part of Scott's army during the seige of Mexico City. Ward was seriously wounded at Churubusco. They had a tough time of it, only about one in five of this regiment survived the combat and sickness that met them in Mexico.
For openers, you may want to track down A. Lombard, "The High Private, Exciting History of NY Volunteers and the Mexican War." (1848). Paul Foos' book "A Short Offhand Killing Affair" (Uni. No. Carolina 2002) should be much easier to find and has a detailed account of the organization and sailing of the regiment to Vera Cruz. I think that you will find much useful information in Foos book. Let me know should you need more information.
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