Not sure if they get recycled out, so this may not be accurate in the future. For me, I found the easiest Featured Contract. It is called "Final Test Contract". It is the last one in the list of them. All you have to do is eliminate the guard at the gate and the guard in the booth at the start of the ICA Facility. So spawn, immediately shoot them both and leave. Takes less than 20 seconds.
To get to featured contracts, from the menu, press R1 to scroll through the menu options until you reach Contracts. Then scroll to Featured Contracts and look for "Final Test Contract". Hopefully it doesn't get changed since it is so easy