Here is another book that reproduces Hamilton's infamous quotation on what he valued in a minister:
He is just what I should like for a military parson except that he does not whore or drink. He will fight, and he will not insist upon your going to heaven whether you will or not.
Hamilton didn't become an orthodox Trinitarian Christian until the end of his life, after his son died in a duel. During the time in which Hamilton did his work Founding America, he believed in a generic, naturalistic religion that might be called theistic rationalism. As he put it in The Farmer Refuted (1775), the quintessential theistic rationalist position:
The sacred rights of mankind are not to be rummaged for, among old parchments, or musty records. They are written, as with a sun beam, in the whole volume of human nature, by the hand of the divinity itself; and can never be erased or obscured by mortal power.
Elsewhere when describing what he looked for in a wife, he likewise explicated this generic religion. As he wrote to John Laurens in 1779:
As to religion a moderate stock will satisfy me. She must believe in God and hate a saint.