Passports for every travelling family member, the marriage certificate, birth certificates for each child, the principal's petition and approval evidence, and any previous US immigration records. Add proof of an ongoing relationship where the marriage documentation is old or issued in a different name.
Prepare for two different audiences
One set of documents supports the immigration applications; another answers a future employer's verification process. They overlap but are not identical, and the second is usually overlooked until the spouse has an offer in hand. Keep clean copies of the arrival record and status evidence accessible rather than packed in a container.
Where a name differs across documents because of marriage or transliteration, obtain the linking record before leaving. Deal with name discrepancies before departure rather than after, because they are the most common cause of an otherwise complete file stalling. A marriage that changed a surname, a transliteration that differs between two passports, or a birth certificate naming a parent differently from a current document all need a linking record, and those records are usually held by the registry that issued the original.
Obtaining one from abroad after the family has moved is slow and occasionally requires a local representative. Identify every such mismatch during the first review and order what is missing while it is still easy.