Cleaning the grease off the engine...

Any recommendations? Should I even try to do this? I tried to clean the engine on a car of mine once before with some scary and not so great results. The manufacturer's engine coating was ruined after that.

I would say if it was that bad you should spray it with some engine cleaner and spray it off with a garden hose.
I keep my engine clean by spraying it with SUPER CLEAN a couple times a year and spray it off with a garden hose.
My engine is always clean.