The reason you read so many different things is that we all do different things. For many people whatever they do is "the best" but you get different "bests" from different people.
I don't like to use sharp gravel. The chickens scratch and can cut their feet on sharp gravel. My run is dirt but when it rains for a while parts can get muddy. I dump round pea gravel in certain areas so I can walk without sinking in and getting muddy. The round pea gravel doesn't hurt their feet.
Before they were domesticated chickens were walking on dirt. The problem in a run is that they are confined there. They will destroy all vegetation and it can get muddy when it gets wet. Mine drains pretty well (it is on a high spot) so I'm OK with mine. You don't want it to stay wet, that is unhealthy. Wet is going to be your biggest potential problem with a run if it gets wet and stays wet long.
Some people turn their run into a compost pile. They dump grass cuttings, leaves, garden wastes, even kitchen wastes in there. The chickens keep it turned for them and find things to eat in there. Some really like their wood chips. Some use sand but usually have to remove chicken poop on a regular basis to keep it from stinking. Others use different bedding.
