Step 1: Sort each option by its arch using the nerve rule. First arch muscles take the trigeminal nerve, second arch muscles take the facial nerve, and the levator palatini comes from a more caudal arch supplied by the vagus.
Step 2: Buccinator and stylohyoid are moved by the facial nerve, placing them firmly in the second arch. Levator palatini is not a trigeminal-supplied muscle, so it is excluded from the first arch.
Step 3: The anterior belly of digastric is innervated by the nerve to mylohyoid, a branch of the mandibular division ($V_3$) of the trigeminal nerve, which is the signature of a first arch muscle. This matches the question.
Step 4: The first pharyngeal arch derivative among the choices is the anterior belly of digastric.\[\boxed{Anterior\ belly\ of\ digastric}\]