Citrus degreaser is fine for the chain - you don't need anything stronger. A friend uses Simple Green. Same idea.

I always take the chain off if I am doing a good cleaning. And the cassette. I just did it all this afternoon. I use an ultra sonic heated cleaner, but you can also put everything into a tub of hot water/cleaner and put it on your clothes dryer while running/vibrating. If you take the cassette off use a zip tie to keep the pieces together in order!

To clean hands afterwards, we use "Zep heavy duty hand cleaner" with pumice. It is gritty, but cleans very well. I don't mind a little grease under the fingernails as it is cheaper than a manicure!