You can control any motor with any method that will handle the load. But you must still provide overload protection if not provided within the motor.
Most most motors that have internal overload protection are usually up to around 3hp single phase. A typical starter combines control with overload in one assembly.
If your motor has overload protection within then a contactor without overloads is acceptable and cost less.
Branch circuit switch or breaker could also be the control device. May not be a good practice in some cases but is allowed.
The controller shall have a rating as specified in 430.83(A), unless otherwise permitted in 430.83(B) or (C), or as specified in (D), under the conditions specified.
(1) Horsepower Ratings. Controllers, other than inverse time circuit breakers and molded case switches, shall have horsepower ratings at the application voltage not lower than the horsepower rating of the motor.
(2) Circuit Breaker. A branch-circuit inverse time circuit breaker rated in amperes shall be permitted as a controller for all motors. Where this circuit breaker is also used for overload protection, it shall conform to the appropriate provisions of this article governing overload protection.
(3) Molded Case Switch. A molded case switch rated in amperes shall be permitted as a controller for all motors.