Sure, mechanical relays are cheaper but sometimes they can send some high voltage back into your controller. You can take precautions by adding other componants into the circuit, not sure exactly what because electronics is something I have a very limited knowledge of, but I think you can use a diode or run a resistor over the coil.
The point is, SS relays are not a big money item so it's best to use them. Another advantage is speed. A SS relay can switch much faster than a mechanical for flickering lights or fast cycling valves. SS relays also last longer. SS relays are quieter, mechanical relays click loud enough to be heard when they are activated.
They are easy to use. Just wire the output of the controller to the input side of the relay, and wire an electrical cord to the output the same way you would wire a switch. That is, split one wire and connect each side of the split wire to the output terminals of the relay. Then plug the cord into an electrical output.
The relay acts as a switch turning the power on an off, except instead of you turning the switch on and off, the controller does it electrically.
I can take a picture of the wiring if you are still unsure about it.