Which type of Relay is good for switching AC water pumps?

The issues are:

1. Transient kickback voltage from inductive devices, mostly when you want to open the circuit, ie turn off.

2. Inrush current to stalled motors etc.

3. Noise.

4. Driving a large relay from a uP.

As Mark pointed out, contactors are the standard solution but those with AC coils invariably buzz loudly in time. But they have big metal contacts that will take the abuse of switching nasty old motors and such, except not at a high rate on and off. For that you need mercury relays.

You might be able to drive a Solid state relay directly or with a small driver chip but it has to be big enough to snap the circuit breaker without blowing up, ie use at least a 25A SSR on a 15A breaker. Note that the size of the motor is not an issue here as long as the relay is bigger. The current spec for the relay depends on the breaker, not the motor. It may also need a MOV across it to keep it from retriggering from the load kickback. ie switching on but not off. Hope rthis helps.

A contactor IS the prefered option.... If you are considering a solid state relay then i assume that you want to turn the pump on and off at a fairly quick rate. ( i.e. more than once in a 20 minute period) short cyclicing a pump will cause it to over heat and it also consumes more power than one running continously.

It would help to have a better understanding of how you plan on operating the pump as well as the. Size of this pump.....

A microcontroller has only a few milliamps(5 to 30 ma) capability per pin with which to control a device. Thus you cannot directly control a large item like a contactor whixh can demand a half amp or more to activate.

What you can do is dasiy chain a smaller device to control a larger device. A simple transistor can boost the current handling output of a microcontroller pin by a factor of 50 allowing a small relay to be operated. That small relay in turn operates a much larger relay like a contactor.

If you want to control a larger voltage such as 110vac consider using an opto isolator. This is a device that uses an led to operate a light sensitive transistor. Because light is use as the control you have complete electrical isolation between the two power supplies. This is the basic theory of operation of a solid state relay

you are switching a highly inductive load frequently, a solid state relay may not designed with transient kick back, i suggest pick an electromagnetic relay with silver cadmium oxide coated contact for long life