I use Simple Green as well.
I put full concentration simple green into one of those chain cleaners you hang off the chain and run the chain around and around. Then I rinse it off, dry it and re-lube.
Comes out very clean.
I usually use kerosene for chain cleaning- I put it in one of those nifty clamp-around-the-chain-and-turn-the-crank-type cleaners I got some years ago- like bakechad has- and it still works good (wonder if they still make it???).
Kerosene works for me, YMMV.
Brake cleaner is kinda nasty for the application.
I used Simple Green (neat) and a brush. This should get a lot of the grime and water soluble salts. Then I rinse, wipe down (dry it off) and soak in WD-40, then another brushing. This will get the residual oils and most of the waxes. Then another wipe and I suppose if you have some waxes left, do a brake clean blast.
I've been lubing with Amsoil MP and Heavy Duty MP lately.
I should have said the Park chain cleaning tool. It clamps over the chain.
I use one of those sometimes. Other times, I just use Simple Green or a citrus cleaner.
I'm using White Lightning Clean Ride wax lube this year, we'll see how it does. I usually use Tri-Lube, though last year I used White Lightning Epic and liked it a lot.
Little behind on this one. Simply use Dawn dish detergent full strength. Dribble the soap on there and let it sit for a few minutes. Coat the cassette too. Then, take a regular old stiff brush and hold it on the rear cassette while rotating the chain backward. Rinse and repeat if necessary.