When fighting regular humans, the most he should do is toss them.
When fighting people he doesn't particularly want to hurt, but has to, he should be primarily defensive. His objective should be to end the fight as soon as possible. He could ether allow them to exhaust themselves or use as few offensive maneuvers as it takes to put them down.
When fighting against people he absolutely has to stop (like Zod)...I think JLU pretty much got it right. However, I'd them to expand on that and allow him to use everything in his arsenal. Flight, super speed, heat vision...all of that. He should also use his elbows, shoulders, and knees. His style should be all about power and brute strength. Landing hit after hit after hit.