The Amazon page, the specs section and the datasheet all clearly state the valve power supply as 9-24V AC/DC. So it’s not DC only but the relays cannot handle AC so let's not get things any more confused than they already are. 12V DC is supply voltage to use.
The Amazon power supply you referenced here is a good choice for the permanent installation.
Only one relay is required as the valve has it's own internal relays to turn off power when it reaches either end of travel. I do not have a decent spec sheet for those relays so my drawing isn't the best but it should give you an idea of how the valve is wired to the relay.
edit: Originally, brass always contained a small amount of lead. That is until the peoples republic of California decided the minimal amount of lead was poisoning their subjects. So, all the plumbing fitting manufacturers had to reformulate their casting lines. About five years ago, there where brass fittings you just couldn't buy as lead was eliminated from the brass. Now things are back to normal with everything available in lead free and regular brass. Most of the 1/2" and 3/4" valves/nipples/unions/etc are only available in lead free, especially in the big box stores. Larger stuff is available for non-potable applications, it is always cheaper and is marked "not for drinking water".
