Can anyone identify this type of shutoff valve?
That is a standard sweated valve, if it is leaking they are easy to repair and much cheaper than a new valve. Most of the time a new seat (rubber seat that stops the water) and a new stem packing under the nut that holds the stem in place is all that is needed to fix a leaking valve , if it is leaking at the hose fitting that was probably over tightened , the plastic ones today break when over tightened those metal ones sometimes held but it looks like it is leaking. , replacing the valve with a 1/4 turn you will probably have to replace the hose also. I have a kit of faucet seats and valve packings / gortex rope that I got many years ago 10$ fixed probably 30 valves I still have the nice little metal box and buy rubber seats to refill you might consider a valve repair kit as looking at the age your home probably has 15+ total valves you could repair for the cost of 1 or possibly 2 new valves.