The Olympic Press is the Best Overhead Pressing Movement. It works the most muscle mass and, if done properly, moves the most weight. After reading starting strength I’m convinced it’s the safest Press of any Sort.
But Variety is the Spice of Life.
Seated Presses put more work on the shoulders.
Arnold Presses have a greater ROM and arguably
hit the most muscle fibers in the shoulder.
Alternating Dumbbell Presses demand even more stability than the normal Press.
The Push-Press allows more weight to be used and more reps can be done in less time.
Good Shoulder Press Machines like the ones made by Hammer Strength are great for flushing the muscles with blood while still using heavier weights than one would use for Dumbbell Lateral Raises.
IMO the best Overhead Press after the Olympic Press is the Grappler Press. Use a Grapper, Landmine, or just throw a bar in a corner. Put 1/2 the plate weight you’d use for a Standing Press and then press that end of the bar. If you tend to over-arch while Pressing or you just want something new then this is a good exercise that I only see Dave Tate and CT doing.