Since the shutoff valve is leaking (the packing inside is worn), I'd like to replace it. Is the valve soldered onto the supply pipe, or is it a threaded connection?
That looks like a 1/2" copper pipe with the valve soldered on. Definitely check it with a magnet before trying to wrench it off.
If it is copper and you are not handy with soldering, you could replace it fairly easily using a valve with a compression fitting inlet:
You will have to carefully cut the pipe behind the existing valve, and use steel wool and/or some emery cloth to clean up that oxidation/corrosion on the copper pipe.
My personal preference is to solder a threaded male adapter onto the pipe and using a new threaded supply valve with 1/2" FIP inlet:
You can try a magnet to the pipe to see of it is an iron or steel pipe. The magnet will be readily attracted to the iron pipe. Copper will not be attracted by the magnet. From the looks of it in the picture I would say that it is a galvanized iron pipe.
An iron pipe will have a threaded connection to the valve. To properly remove the valve from the pipe extension you are going to want to use two tools, one to keep the pipe extension out of the wall from turning and the other to turn the valve. An appropriate tool for keeping the pipe from turning will look like one of these:
The tool to turn the valve assembly could be one of these:
The reason it is so important to keep the pipe extension from turning is so that you do not loosen the threaded connection in the wall which could lead to a leak there.
When you have the valve off it would be a good opportunity to replace the very rusty escutcheon plate that is against the wall.
That looks like a Brasscraft valve. I bought a repair kit at Home Depot (Lowess didn't have it) for a few bucks. Pretty easy to install and that fixed it. Here's a link to a Dano (aftermarket) repair kit: http://www.amazon.com/Danco-88001-Repair-Brasscraft-Stops/dp/B000HE6OPE/ref=sr_1_3?ie=UTF8&qid=1416804275&sr=8-3&keywords=brasscraft+stop+valve+repair+kit