Your listed cleaner will work. I use Shooters Choice and just wipe it down and scrub it out with an old tooth brush. just be sure to oil and lube the slide rails, lugs and leave a light coat in the barrel to prevent rust. Then shoot it alot and have fun.
Cosmoline is that gunk a gun is covered with to prevent corrosion. A gun isn't sold immediately after it is made. It sits around a lot. The only reason most people don't see it is the dealer has cleaned it up for show in his store.