Check the weather. If it won't be too hot at the bottom, I suggest starting right at first light. The first five miles are the most scenic and it's a shame to go past it in the dark. On the other hand, if it's going to be hot in the bottom, heat exhaustion is no fun either. Arrive at the trailhead early enough to get a parking spot. Take electrolyte replacement and stay hydrated. There are two routes up the south rim from the river. Take the route that has water - Bright Angel I believe. The other route doesn't have water and is longer as I recall. I second the suggestion to hike in trail running shoes.