Branch circuits are protected by the circuit breaker found in the electrical panel. Each circuit should have its one breaker. The breaker should be rated to protect the insulation of the wire, so you can determine the breaker size based on the circuit conductor size Example #14-2 should be protected by a 15 amp breaker
You use the correct size breaker depending on the size wire in the circuit. If the circuit is wired with AWG #12 wire use a 20 amp breaker. If it is wired with AWG #14 wire then use a 15 amp breaker.
A 15 amp dedicated circuit breaker should be used for the dishwasher. The disposal can be wired to the general kitchen 15 amp circuit.
The pool light is usually on a 15 amp circuit. The breaker feeding this circuit must have a GFCI rating.
The wire!! The breaker is there to protect the wiring not the device plugged into the circuit.
The size breaker you use is determined by the size wire used in the circuit. If you use AWG #12/2 wire then use a 20 amp breaker. If you use AWG # 14/2 then use a 15 amp breaker.
A circuit breaker protects the wires that the devices are connected to. If the devices that are connected to the circuit are 20 amps the wire size should be #12 wire fed from a 20 amp breaker. This breaker should not trip unless the circuit is overloaded or a fault occurs on the circuit. If the devices that are connected to the circuit are15 amps the wire size should be #14 wire fed from a15 amp breaker. This breaker should not trip unless the circuit is overloaded or a fault occurs on the circuit. Putting 20 amp sockets on this 15 amp circuit will work but the circuit is limited to the amount of load that can be plugged in. You will not get the full capacity of the 20 socket because the breaker will trip at 15 amps.
The sizing of the circuit breaker and hence the wire size to feed the pump are all dependant upon the amperage of the pump. This question can not be answered without that information.
Suggest dedicated 20 A circuit.