It depend on the targeted application (propulsion, electricity generation, etc.). There are two main type of induction machines (the squirrel cage and the doubly-fed induction machine). If you are interested by renewable energy conversion (i.e. wind turbine), the doubly-fed induction generator is the good candidate. If you are studying vehicle applications (i.e. electric vehicule), the squirrel cage induction motor is a good solution.
As regarding the study of induction motors, then squirrel-cage ( both in single-phase and three-phase) and wound rotor motors should be studied. The wound rotor induction motors are also called slip-ring induction motors. Usually, the small induction motors are squirrel-cage type while the large motors are of 3-phase slip-ring induction motors.