In times past, coaching collars meant "choke chains", a metal chain with a sliding ring fastened to your dog's leash. Used by an experienced coach, a choke chain is fine and dandy. The problem starts when amateurs try to use them. In truth, Mr Average has no conception of how to use a choke chain in a safe manner. Personally, I prefer a buckle collar, in nylon or leather, which can be employed for coaching as well as for everyday use. It should fit nice and snugly, but leave enough space for you to put a couple of fingers between the collar and the neck of your pet. The choice of material is basically down to you - nylon comes in many attractive colors, and is particularly good for dogs that like to splash around in the water (or worse things!!!).
By the same token, if your dog is a Rotty, a ritzy diamante-studded poodle collar is going to look ludicrous, and trust me, dogs can develop neuroses too! Whatever you choose, always include an ID tag. If your dog wanders off, you have a much better chance of getting him returned than if he is tagless. In fact, without a tag, he'll probably end up in the pound, and you may never see him again.
Alternatives to choke chains include the 'harness' - a halter that fits round the neck and ribcage. This eliminates any chance of the dog choking. Harnesses are particularly useful if you have a BIG woofer - a mastiff or Irish Wolfhound, for example, that likes to pull strongly when you are out and about. Strangely, harnesses also work well on the smaller breeds, which can suffer injuries to their fragile windpipes far more easily than the more robust types of dog. As with collars, the material the harness is made from is yours to choose, and as with collars, it's basically a matter of your own personal preference.
The more expensive models have meters of leash, and a "braking" system operated by a button on the handle. This stops your dog from running too far, while allowing you far more 'play' than a standard lead more...