For more information, how much multiple horse driving experience do you have? With experience, what kind of equines have you driven, large, small, draft, chunk ponies or the more streamlined ones like QH, Standardbreds, Welsh or Hackney?
My first suggestion would be to get some lessons. Having a trainer working with you will certainly aid your driving confidence, widen your experiences with multiples or a single. Refine your technique with whip, rein handling and READING your horse in situations.
There are a GREAT many horses and pairs of horses available, from all over. They come with all kinds of skill, training and exposure to outside things a road driver could run into. Whether you want them to come live with you, deal with their previous training, good and bad experiences, is going to be your choice.
Trainer lessons can aid you in being a better looker, more observant and knowledgable, in dealing with various horses you try driving at try-outs while shopping.
Do you have equipment from previous animals you might wish to keep, fit to another new horse/s? If you already have lots of stuff, you may want to stay in a certain size range to avoid purchasing MORE stuff. Maybe you wish to change over totally from draft to carriage style things? Sell all and buy new to fit, new horses? You have to decide.
Looking around, visiting trainers, other horse gatherings, lets you see more variety of vehicles, harness styles, before you jump in and buy. Write down names of makers, take photos for later viewing, comparisons, in the search of RIGHT-for-you equipment. Consider breed specialties that may be hard for you to work with in your area. Draft folks have shoeing problems in finding farriers, pay much for good work. Saddlebred, Hackney, Morgans, may have a problem finding a farrier who will leave foot long enough, to put on shoes they can work in. Many less expensive farriers think they will please the customer by trimming short, using too small of shoes, so horse has small, cute hooves. Creates huge hoof problems for a working animal. Those farriers don’t understand the needs of the breeds, bred to have sturdy, good sized hoof under them. You may or may not have better farriers in your area and then be able to get them out. Above breeds and ponies are pretty tough footed in most cases, perhaps you could even leave them bare for moderate driving on softer surfaces.
I know in our area, a GOOD draft farrier is REALLY hard to come by. Few farriers will even look at drafts, also hard to get working on the half-drafters. Fancy moving horses, bigger hoofed, naturally longer toed like Saddlebred, Hackneys, Morgans, can be hard to find GOOD farriers for as well, even going plain shod, not breed ring or Park. Something to consider when choosing. I LIKE those 3 breeds, but they do need people who know what their hooves should look like, working on them.
I would suggest again, starting with some driving lessons with a knowledgable carriage driving trainer. Gain experience, more knowledge before shopping for horses. Don’t beat yourself up too badly, some horses will never drive safely, whatever training you would give them. Doesn’t mean you failed, maybe more that you didn’t read them correctly.
Hitching a horse and being ABLE TO DRIVE a horse safely, are two WAY DIFFERENT things. Trainers see so many more animals, they have developed a more critical eye, faster at seeing the cracks in horse attitude of a poor driving candidate.