Underbelly heat is best for most snakes, including kingsnakes. Attach the heating pad under the glass at one end of the tank and put one hiding place at the warm end and another at the cool end so that the snake can thermoregulate itself properly. In the wild snakes spend most of their time NOT being seen (a behavior that helps explain why they have been so evolutionarily successful). The main reason for lighting is to help YOU see the snake. You should also have a non-tippable shallow crock of fresh water for the snake at all times.
The only thing more important than a temperature gradient and places for the snake to hide is an escape-proof lid/locking mechanism. Snakes are EXPERTS at escaping and, as mentioned before, VERY good at not being seen. If your kingsnake is not already eating frozen (then thawed) mice, try to switch it from eating live mice as soon as you can. The way snakes suffocate their prey is efficient, but not all that quick sometimes. The mouse can suffer, not to mention that it can bite the snake and leave scars, or worse, an infection.
You should check out some breeders' websites, which often have care sheets that give more information in greater detail. Enjoy your new acquisition!