The project consists of controlling a 24V on/off pneumatic solenoid valve using arduino UNO. The problem lies in supplying enough current (~130 mA) to the solenoid valve, without damaging the arduino, but not too low so as the solenoid valve not working. After doing some research it was suggested to incorporate a relay in the circuit set up. Does anyone know if this relay-incorporated set up will work? And if it does, how will the circuit will be connected? And what voltage rated relay to be used?
Yes a relay will work but that is totally unnecessary. Use a simple transistor to switch your solonoide. A googled search will give you the circuit, it consists of one transistor and one resistor.