"Peter" is the subject of the verb "are needing" -- and so is the pronoun, which should therefore be "I" rather than "me".
2. Verb tense:
For something that is generally true and not specifically ongoing, use the simple present tense ("need") instead of the present progressive ("are needing").
3. Relative Pronoun confusion:
"Who" is the subject pronoun, but in this case we need the object pronoun, which is "whom". This may sound a little too formal in this case, but it is important to understand the grammatical rule.
4. Apostrophe confusion:
In this sentence, "it's" is meant to be possessive. And this is normally how we signal the possessive: by adding an apostrophe s. For example, the possessive form of "envelope" is "envelope's". "It", however, is a special case. By adding an apostrophe s, we are indicating that the word is a contraction of "it is". If we want the possessive form, we just add the s: "its".
5. Word confusion:
Be careful not to confuse "than" with "then". "Than" is used in comparisons; "then" is used to order events in time. Also, be careful not to confuse "to" (a preposition) with "too" (an adverb).
6. Verb form:
"Being posted" is the progressive form of the verb, which is easily confused with "been posted" (the passive form that was intended). Here, however, the passive voice is not our best choice. Instead, we should use the active voice in the simple present tense: "post" (cf. comment 8 below).
Whether we say "the United States" or just "the States", we are referring to the name of a country, which is a proper noun that must be capitalized.
8. Passive voice:
As a rule, it is better to use the active voice as it usually makes the the meaning clearer. Instead of saying "it's written", we should say "we write"; and instead of "posted by us", we should say "we post".
We write the address "on" the envelope, not "in" it.
Peter and I need to know whom to address the letter to before we write on its envelope and post it to the company in the United States.