I think it's the hot water side. I guess I have to turn off the water, cut the pipe underneath the connector, put on the valve, then turn the water back on. Any steps to take before or after turning off the houses water?

What kind of valve should I buy, exactly? I wanna get a sharkbite version because soldering underneath there would be tough (and I dont have a lot of experience soldering). Here are some pics; i have no idea what the little black wire/thing is, but the hose that attaches to the faucet is off (you can see the hole in the top). Its old as heck.

Thanks a ton!