I find that a capacitor is provided on a ceiling fan, and I am told it is meant to start the fan motor. Fans are there with different blade sizes, so the motor sizes must be different. How is the capacitor to be selected? Does this capacitor play any part when the fan is running?
If capacitor size is large what will happen? If it is small then what will happen?

Most ceiling fans use a permanent split phase capacitor motor (PSC). The same cap is used for running and starting. The capacitance determines speed. A higher capacitance, the faster it runs. Capacitance adds when placed in parallel, therefore many ceiling fan caps have 3 leads and use two different capcitances. One, the other and both give you three different speeds.

Optimum size - never thought about it.

The capacitor size is specifically matched to the stator. You cannot use a larger value capacitor without overheating the motor. A lower value capacitor will cause the fan to run slower, this is how they use capacitors to derive medium and low speeds.