Best for the chrome grates? Stainless scrubby pad after a overnight soak in dish soap and water. Best for the expanded steel upper grates? Same soak and a wire brush, the cheap kind you use for removing paint. Like $3 at Home Depot. I use a dish cleaning brush to get in the tight spots on the grates.
Then rinse, dry, spray with cooking spray like Pam.
Honestly, the grates don't need cleaned spotlessly every time. I take the stainless pad and scrub the chrome grates after the cooldown to get chunks off and use the wire brush on the upper grates. I'll do the soap/soak a few times a year.
I'd be hesitant to use stainless steel scrubby on chrome. They will eventually scratch chrome off.