Number 12 wire is the correct size for a 20 amp breaker. It is not required, but you really should use a 20 amp outlet as well even though a 15 amp outlet is legal and acceptable. You may run 14 gauge wire to a switch and then to a light, but ONLY if the circuit is on a 15 amp breaker. You may NOT use #14 wire to go from that outlet on a 20 amp breaker to anywhere at all.
The circuit breaker size determines what size wire to use, not where that wire originates.