You don’t need fancy chemicals. Just grab a soft sponge (never steel wool, you monster), a bottle of white vinegar, and some dish soap.
Also, get a clean bucket or bowl. And a towel—you will spill. Trust me on this one.
If you have a cooler with a tap, you might want an old toothbrush. It’s perfect for scrubbing those tiny crevices where mold goes to start a family.