Hook Types

With the exception of circle hooks, the hook setting effort is roughly the same on all hooks. Circle hooks brought a revolution of sorts to the fishing industry. They are curiously curved back on themselves and are advertised to hook fish "in the corner of the jaw". Most anglers using circle hooks agree that they do prevent a swallowed bait from becoming a gut hooked fish. They have decreased the catch and release mortality rate significantly.
These hooks work without a hook set.

As the fish takes your bait, simply wait until the fish is moving away from you. Start reeling slowly at first, increasing the speed as the fish applies pressure. The design of the hook allows it to be slowly pulled out of the throat of the fish and to the side of the jaw. As the hook shank comes to the mouth of the fish, it turns, allowing the point of the hook to penetrate the jaw. No hook set is required!

Because billfish swallow the bait, billfish anglers have gone almost exclusively to circle hooks, allowing a clean catch and release and very low fish mortality.

Setting a circle hook when the fish bites almost always results in a missed fish. The re-curve of the hook point prevents it from encountering a solid surface, and the bait is simply pulled from the mouth of the fish.

Bait

Anglers need to size the bait to the fish they pursue. A large dead bait will only be cut to shreds by smaller snapper or bottom fish. That peck, peck, peck indicates smaller fish tearing away at your bait.

If these are the fish you want, move to a smaller hook and smaller bait. Then, as they swim away with the bait, set the hook and reel.
Artificial baits - lures - usually have more than one hook and those hooks are often treble hooks. With the exception of deep-water jigs, these hooks are smaller than the conventional bait hooks you might be using, and consequently they can be ripped out of a fish if too much pressure is applied. They will generally hook themselves at the strike of a fish, and playing the fish with a proper drag setting becomes very important.

Live bait is just that. These baits are usually hooked so they can swim freely, and that usually means a smaller hook than you would use for dead or cut bait. When this bait is taken - when you get a bite - you need to hesitate a few seconds to allow the fish to get the entire live bait into its mouth. In general, only when you feel the fish swimming away from you should you set the hook. If you are using a circle hook with live bait, simply begin reeling a few seconds after the bite.

Dead and cut bait are used with slightly larger hooks than those for live bait. Once again, wait until the fish is moving away from you to set the hook.

Water Depth

Line stretch is an issue that escapes most anglers. With the exception of several brands of "no stretch" braided line, all fishing lines have a stretch factor. Monofilament line, the line most commonly used, has a significant amount of stretch and the longer the line, the greater that stretch.
Fishing in deep water, water over 50 feet, requires that hook sets on standard hooks be significantly more powerful than those in shallower water. The angler must make up for the line stretch.

Many times an angler will set a hook on a deep water fish, reel several cranks and set the hook again. The idea is to apply enough pressure to overcome the line stretch and allow the hook to penetrate the jaw of the fish.

Sometimes a sinker weight of twelve ounces or more is required to get your bait to the bottom. That sinker, coupled with the line stretch will absorb the hook set pressure, and that means a missed fish.

When fishing in deep water, be prepared to hit the fish hard and heavy to overcome the stretch factor.

Pure Physics

In all of this discussion, the physics of line, hook and direction are at play. Setting the hook on a fish moving toward you will almost always result in a missed fish. Additionally, when the fish is moving away from you, that movement adds to the power of the hook set. Line stretch, water depth, bait size, and hook type all have an effect on how the hook will penetrate the jaw of a fish.
It takes practice to "feel" the fish and know when to set the hook and when to let the fish run. Many anglers say, "It's a small fish pecking around" on a bite because they have experienced the difference between a good sized fish and those little bait stealers. It takes practice and time to tell the difference.

The great part about gaining this experience is that you have to fish to learn!