To clean my chain I spray some WD-40 (I have the biodegreaser too but the spray is more convenient), wipe the chain with a rag, wipe it again, and add a drop of oil on each link spin the chain a bit, and wipe it again carefully.

I tried the trick where you remove the chain then shake it in a bottle w. degreaser. I found the chain to squeak more after that. I think that cleans it too well and it's difficult to put the lubricant back between the rollers and pins. Plus I'm sloppy with a chain tool.

Oh and fenders/muflaps help a lot to keep the chain cleaner after a ride on wet roads. I could tell/hear the difference after I installed fenders.