If it's standard, non stabiliser hitch, then grease it. Don't really matter what grease. I find easiest is the aerosol spray lithium grease. Spray a bit on ball before hitching.
However, with a stabiliser ... don't put any lubricant, of any sort, anywhere near it. Always clean it before hitching up, if it's been out of use for some time.
I usually smear a bit of engine oil on my towball before hitching up. Mine isn't a stabiliser hitch (which need to be clean and dry as already stated by others).
------------- Give a man a fish and he'll feed his family for a day.
Teach a man to fish and he'll sit around on a boat all day drinking beer!
Ours is a bog std trailer hitch, so I always Grease, with whatever Grease I have in the workshop, if nothing else it stops the Hitch from sticking, and makes detaching easiar.
I have never greased it even though the hitch is not a stabiliser type. My thinking is that I don't want the hitch really easy to move as it will make snaking easier.
Just remember the purpose of grease or oil. My old tech teacher always said what keeps bricks together? We would answer cement! No he would say, cement keeps them apart! And that folks is the purpose of oil or grease. It keeps moving parts away from one another and therefore less friction and wear. Kelper is correct, if no stabiliser then grease/oil. It will ruin the stabiliser if oil/grease gets in because the stabiliser needs friction to work. Here endeth the lesson sorry to be such a bloody know-it-all!