For small mini you really don't have a lot of choices. You need to be concerned about the weight of the cart, especially starting out and you need to be concerned about the size for both the horse and the driver. Most "A" size carts will have 20" wheels and 46" or 48". shafts. You are probably better off to have 48". with the idea that a little too long is much better than too short. The 20" wheels are pretty much standard and will roll easier than smaller ones. That is pretty much the only variables you'll have any control over, and a cart with those dimensions is very common. You'll need to be concerned about the height of the shafts as you want the cart to sit level when put to the horse, so try to get a cart that can be adjusted for height. Most are limited in adjustment, but you can usually lower a cart by placing the axle inside the frame instead of of under the frame and can lower it by about an inch or two. Try to get the shafts as level as you can for balance to make it easy on the horse.
The other considerations is to be sure the driver fits the car. Many are downsized to fit the horse with no concern for an adult driver. Look for an adjustable seat and try it out to be sure you can sit comfortable and si in it with someone holding the shafts level to check for balance.
Good Luck.