Help choosing a relay for pump control
Anything you do with 120VAC must be Code legal.  Fortunately, you can raid the parts bin of the heating/cooling industry, stuff that's safe, code legal and cheap because it's made by the millions.

Think the way a smart thermostat works: use the Arduino to switch 24VAC control power.  Then use the 24VDC circuits to control large power contactors to switch the motor.  This also keeps 120/240V far away from your Arduino. 

Here's a common 24V transformer.  Notice how it screws into a 1/2" knockout on a steel junction box.  That satisfies Code requirements to keep low-voltage wiring separate from 120/240V.  

Switch the 24V with the Arduino, then at a workable location along the 120V wiring, install a steel junction box to contain a suitable A/C contactor or fan-control relay. Run the 24V wire to it, that can be thermostat wire and you can legally run it the same way.