best advice is to do what's most comfortable. have your athletes push off from both legs, so they know how to react when they get to the water jump and something goes wrong. Also, try standing in front of them, or put cones in certain zones to force them to jump/ land in different areas. races are never like practice where it's just one person in the take-off and landing zone by themselves.
hurdling the water jump is quicker overall, and can save about a half second, but i noticed that the biggest boost came in adrenaline (both from me doing it), but also the crowd factor. they usually gave a big cheer. that's the best part of the steeple: it's the only distance race that non-distance people like to watch, so the crowd is in your favor. use them to your advantage.
when pushing off the barrier, many people mistakenly go up, and then drop, leaving their arms way up high. make sure to teach your athletes to really extend their push-off leg (it may seem counter intuitive to keep the foot on the barrier for that extra half second), but the goal is to the leg as a lever to push the body off the barrier. allow the body to catch up to the foot, to use that momentum and reduce the leg's work in pushing. if this is done properly, momentum will be naturally carried all the way through the water jump and will allow the athlete to resume natural running speed within 1-2 steps. this is the best place/ way to drop an opponent.
The arms are integral to pushing off correctly, and it's pretty simple to coach: teach your athletes to keep the hands under the arm-pits. Simple as that.