That is listed as 12V DC solenoid so you definitely don't want to try plugging into AC mains directly as fire and/or death may follow. Unfortunately it doesn't seem to mention the coil current, if you have a multimeter you could set it to the 10A range and connect it to a car battery with the meter in series to measure.

But otherwise I have a solenoid of fairly similar size (although a gas one) and I just measured it as around 1.5A. I'd hazard a guess those would be under 2.5A so I think a 12V DC power supply with a current rating of 5A would be sufficient for the pair of them.

As you've already sorted out controlling a 5V relay using the Arduino it sounds like the power source is all you need. They are available from most electronics stores, e-bay etc in many styles but here's an example on Amazon.

That is listed as 12V DC solenoid so you definitely don't want to try plugging into AC mains directly as fire and/or death may follow. Unfortunately it doesn't seem to mention the coil current, if you have a multimeter you could set it to the 10A range and connect it to a car battery with the meter in series to measure.

But otherwise I have a solenoid of fairly similar size (although a gas one) and I just measured it as around 1.5A. I'd hazard a guess those would be under 2.5A so I think a 12V DC power supply with a current rating of 5A would be sufficient for the pair of them.

As you've already sorted out controlling a 5V relay using the Arduino it sounds like a power supply is all you need. They are available from most electronics stores, e-bay etc in many styles but here's an example on Amazon.