What are your plans? Are you looking at showing, doing parades, CDE, Roadster, touring around your farm and local country roads?
For local/4-H shows, an Easy Entry "EE" cart is great. It's easy to use, very sturdy, and has a seat built for 2 or 3 adults/kids. They can be customized by recovering the seat and back support, and a can of spray paint. They are not typically used in AMHA/AMHR shows, certainly not at Worlds or Nationals. They run around $400+ and hold their value well.
AMHA/AMHR shows - a "Show Cart" is the norm. This is a wooden shaft cart with bike type wheels and a vinyl "basket." New ones will run $1,200 and up, depending on if you want custom paint. Occasionally you can find a good used one for $900 and up. Some manufacturers are Jerald, Double Diamond, Waggoner (I think they are still around). Very rarely you will find a Houghton, which is IMO the Cadillac of carts.
For a "Roadster" class you will need a show type cart stirrups and with the basket removed, a closed wheel - where there are one or more bars across the entire width of the wheel to protect others if it comes off. There are also regular Roadster carts out there that don't have the basket, just the stirrups.
There are others who manu carts. You have to be careful to check the balance of the cart so it's not too heavy on the horse's back. You should be able to hold the shaft up with one finger with someone sitting in the cart. If you can't, pass it by!
Putting a "wanted" ad on the saleboard might help you find the right cart.
Driving is a blast - have fun!
Hope this helps!