This is a good conversation. To add, I would get one or two circular brushed paint brushes (Autozone offers a quality brush) and allow your product of choice to penetrate carbon and soot deposits. I prefer Purple Power, it’s a strong chemical and works but do not let it dry. Then follow up with some aggressive brushing which will allow you to access those harder to reach areas that a rag (I always use microfiber) wouldn’t.
When done, use a microfiber towel to dry, frequently checking if any dirt is left on the towel. Then, I wrap up with spraying a bit of WD-40 onto a towel and apply it to vacuum and coolant hoses.