Overhead lighting in the gym lets you flood the space with light. You'll want to pick fixtures that are flush with the ceiling since hanging lights aren’t suitable for a space in which you’ll be jumping, throwing, or running.
The two best options are recessed spotlights or track lighting. With recessed spotlights, you can space the lights across the entirety of the room, even if the room is an odd shape, and evenly illuminate the room.
Alternatively, track lighting allows you to angle the lights to different workout zones. Point one light at each machine or piece of equipment, such as the treadmill or weight bench. For the best effect, use a combination of recessed lighting (in front of a mirror) and track lighting (pointed at equipment).