Are there conditions on a Muslim man marrying a non-Muslim woman?

I know that interfaith marriage is allowed by Muslim man to non-Muslim woman from the people of the book. What I want to know, are there any conditions set by the mujtahids on this type of marriage, i.e., whether the Christian belief should be of a specific type. Like for example, if a non-Muslim woman believes in trinity, would the marriage with a Muslim man still be allowed. Please, answers with reference either Hadith or authoritative books from Mujtahids.