I don't think it is too important what you use, as long as the soil in your pot/bed is not exposed.
Outdoors it gets even easier. Here I used some partially composted grass that I knocked off the paving with the weedeater.
In the beginning, it was just mulch, then some grass seeds germinated, the surface of the pot is always nice and cool, the grass uses the sun to grow and cast more shadow without heating the pot up.