Kitchen Sink Shutoff Valve Drip

Where exactly is it leaking? Which side of the valve?

Underneath

Thank you

Usually small leaks like that eventually stop leaking at all.
I'm assuming you have one of those needle valve shut offs, and not one of those quarter turn shutoff.
You could try turning the valve know some and get to where it won't leak, but typically I've found those needle valves have to be either 100% or fully shut off for no leaks at all.

To answer your original question, some plumbers install shut off valves to various locations around the house in the crawlspace or basements. But probably not to a kitchen.

Is it the hot or cold water line leaking?
Sometimes you may could just shut off the water from the water heater and it may keep the hot water lines from leaking.

If it's a leaky valve, I've replaced the valve, but left the original 1/2" nut on the inlet pipe , and just used it with the new valve.
No need to cut off old nut and ferrules

Yes turn the water off to the entire house. Open some faucets that are the lowest in the house and drain the house of water, this may be the kitchen faucet btw. If its a two story house you could have a lot of water in the lines. I wouldn't recommend only a small pan for draining as it could be a lot. Easiest thing is to leave the valve on and drain it out first as that way you can turn the valve off if its overflowing your pan. Then once it has stopped draining, you can pull the old valve and it will drain the last little bit out.

What kind of pipe comes out of the wall OP? Pex, copper, etc?

Your valve could be any number of types, it could be soldered copper which will need to be cut off or most likely its just a nut and copper compression nut. Very easy to just use a wrench to remove and replace.