Horses that show even the slightest tendency toward kicking, rearing, or running back as evasions are probably unsuitable for driving, as is any horse who is uncomfortable in traffic. The perfect driving horse is one that, when frightened, stops and stares at the scarey object, then accepts his driver's reassurance that it's really OK, and continues. This book gives the best overall introduction that I have found to all the different types of driving, how to drive, the steps in training, etc. It will allow you to make intelligent choices about what your goals should be, and will get you started along the right roads. I would strongly suggest that you find and join a local carriage driving club.
Local clubs are the ultimate sources for supplies, advice, things to do, shoulders to cry on, etc.
Sometimes, these clubs advertize in other horsey publications. If you're thinking of training your horse yourself, you really need to take some driving lessons first. It is very difficult to do a reasonable job of teaching driving to a horse if you don't understand it yourself. There are many little differences between riding and driving, and you will be much better off if you learn them with an experienced horse in front of you and a trainer at your elbow. The variety of books mentioned above will provide you with a fairly broad menu of techniques.