Each arch contains a vessel, a nerve, and a cartilage.
1st = CNV (V2-V3, specifically); muscles of mastication, maxillary, zygomatic and mandibular bones, malleus and incus
2nd = CNVII; Stapedius, stylohydoid, platysma, posterior belly of digastric. Stapes, styloid process, stylohyoid ligament
3rd = CNIX; greater horn of hyoid, stylopharyngeus.
4th-6th = CNX; Cartilarges of larynx (i.e. arytenoids), muscles of larynx and esophagus. Actions include swallowing and speaking (recall that the Nucleus Ambiguus is the medullary nucleus that contains motor fibers for branchial arch CNX muscles involved in speaking and swallowing)