Capacitor provided in a single-phase motor is definitely not for imroving power factor, but to provide a split-phase to make the motor self-starting. It could be a Capacitor-start motor or a Permanent Capacitor Motor. Values of Capacitors will vary for Start Capacitor & Run capacitor.
The criteria for selection would be sufficient torque development only to over come the static inertia of the motor & the connected load.
One can refer to Electrical Machine Design by M.V. Deshpande.