The other person's name should come first, "me and John" should not be used. This is manners, not a rule of grammar. The pronoun 'I' is used as the subject of a se
…ntence or a clause. The pronoun 'I' is used as a subject complement following a linking verb (the object of the verb restates the subject). The pronoun 'me' is used as the object of a verb or a preposition. These rules apply whether the pronoun is used alone or as a compound with a noun or another pronoun. Examples: John and I went to the store. (subject of the sentence) He and I went to the store. (subject of the sentence) The shoppers were John and I. (subject complement) Jane gave two apples to John and me. (indirect object of the verb) Jane made apple pie for you and me. (object of the preposition) (MORE) 
