Don't use automobile grease. Get some at the bike shop. They will probably have several brands. They are more expensive but developed for bikes.

You can use spray cans, but it will take many many many coats to give the frame any protection because the paint is so thin and damages easily. If you go to bare metal, it would be a good idea it apply a rust inhibitor first and then several coats of primer with a light sanding with 400 wet-or-dry emory between coats to keep it smooth. (Primer is notorious for shooting out blobs which ruin the final appearence if not sanded.)

You might consider going to an autobody shop and seeing if they will sandblast the old paint off. Don't know what it would cost, but it would be much quicker than tryig to do it yourself if they are willing to do it.