I'm ready to consider hackamore or bridle for my young horse.  What bits (no pun intended) of advice do you have for starting out?

For a hackamore I would suggest anything that has a soft and/or a smooth finish for the piece that goes over the nose. I do not recommend a mechanical hackamore for they do not translate left and right cues very well.

For a bit my favorite is a bit that breaks into 3 pieces for the mouthpiece. It can be a curb with very short shanks (try not to go longer than 3") so that there will be only slight leverage or you could go with a full cheek or D-Ring snaffle where you will not have any extra leverage which is good since it gives your horse a chance to learn progressive stages of pressure. The mouthpiece will be smooth and will have a copper roller and ideally should be made of sweet iron. The reason for this is so that the bit has a good taste to the horse and that way the horse will like having the bit in his mouth to play with.

You may think "why would I want my horse to play with the bit if I want him to pay attention to me?" Horses typically don't think ahead (thus you don't see to many horses playing chess) They are concerned with the present and want instant gratification. When you give a cue with the bit a discomfort occurs and so they then forget about playing with the bit and try to figure out what to do to get rid of the discomfort. Once he moves in a way that is desirable for you, you then release the discomfort and so the instant gratification comes back of the nice tasting thing in his mouth and he goes back to being a happy horse until you again give a cue. Eventually he will remember what he did to get rid of the specific discomfort and will instantly do the thing that keeps releasing it.

Another thing a nice tasting bit becomes is a pacifier when the horse becomes nervous. Have you ever noticed that when you ride and your horse grabs long piece of grass yet doesn't eat it. He just carries it around in his mouth until you either take it out or he goes and grabs a mouthfull of grass to eat. Having something to hold in his mouth is a calming effect and so the bit can be a way of keeping horses more calm.

Just to be fair I'll mention a negative thing that bits cause. Bits do cause the horse to salivate and so they will become more hungary and so they may try eating grass along the trail more often compared to if you were riding in just a halter. However, it can also do the opposite for a few horses in that it curbs the horses urge to eat like chewing gum does for us.

There are many articles on bits and even people have written full books on bits. Each year people try to improve on the bit but the concepts stay the same but still learn what you can so that you can make a rational and educated decision.

To reiterate I suggest a snaffle or gentle curb bit with sweet iron and or copper for the mouthpiece. The mouthpiece should always be smooth and be about 1cm in diameter (or about 3/8th of an inch). Also make sure the length of the mouthpiece fits the width of your horses mouth. You don't want it too small where it pinches your horses cheeks and at the same time you don't want it too large where the cheek pieces don't rest against your horse. If it is too large the cheek pieces will turn and pinch your horse when you lift the reins.