Bits are good options for horses that dislike bitless bridles due to pressure on the facial nerves or issues with rubbing. Bits are also good options for those looking to compete as many competitions require a specific style/type of bit to participate.
Which bit is best? The one that provides the most comfort and least distraction to your horse. The mouthpiece should be made of smooth material. It should not be rough, twisted, or made of chain.
Generally you will want to start with a snaffle. A snaffle is a non-leverage bit. These bits will give you the best lateral control making them the best choice for new riders, green horses, and lesson horses. Snaffles are available in a wide range of mouthpieces including single-joint, french, mullen, or ported. The cheekpieces are also available in a variety of styles including loose ring, eggbutt, dee ring, and full cheek. You will want to add a snaffle hobble to your loose ring or eggbutt if you are riding without a noseband. Full cheek snaffles should be ridden with bit loops. These will keep the mouthpiece in the right position. Without them, the weight of the full cheek will rotate the mouthpiece forward.
Curb bits are leverage bits. They are a good choice for those who ride with a loose rein/soft hands on a well trained horse. For many horses, the curb bit is the most comfortable option. The mildest curb bit is the kimberwick. It has the benefits of a curb and the lateral control of a snaffle making it a good choice for a variety of events.
Pelham/Argentine/D&L Reiner bits are curb bits, and all have the option of riding with your reins in a snaffle (ring next to mouthpiece), curb (ring at bottom of shank) or double configuration (attach a set of reins to snaffle and curb ring). Many people put their curb strap on the snaffle ring of these bits. THAT IS INCORRECT. The curb strap ALWAYS goes on the same ring as the cheekpieces of your headstall.