You need to find out from the seller if there is any finish on the neck. It sounds like there isn't; otherwise, it wouldn't have gotten stained by your sweaty hands so quickly.
You might try to clean the grease off with some naptha. In the US, that is sold in liquor stores and such as "Ronsonol Lighter Fuel," I don't know what you have in The Land Down Under. It is also sold in paint stores. It's a pretty good solvent, evaporates quickly and cleanly, and is pretty benign for any finish. Or you might need to sand it down lightly with 400 grit or higher to remove the stain, and then apply a finish.
What kind of finish to apply is a whole other topic.
Oh, and WASH YOUR HANDS BEFORE YOU PLAY!
Ed