Rules totally depend on which group you show under. Mini horse rules are often different than other horse breed rules or the American Driving Society rules. 4-H rules are not used in other Driving competitions.
You need to decide where you want to show, then find out what set of Rules they use to Judge with. Read those Rules and especially the PICKY DETAILS that specify if you MUST use a checkrein or not, what kind of attire is expected, equipment they want you to use.
With the Rules clearly telling you the information, you can choose the correct vehicle, harness style, know what the Judge will expect in various classes like Reinsmanship. Most ADS classes require wooden wheel vehicles, while other places allow wire spokes. Does make for a lot of reading! A highlighter to mark details will make it easier to find them if you check back.
You might also want to look around for a Driving Trainer, to take some lessons, get an honest critique and polish to your outfit, before showing. There are ALWAYS details in style, ways of doing things, that are never mentioned in Rule books. In Ridden classes, it could be hairstyles and makeup!
The American Driving Society is located here: American Driving Society
Rule book is here to view: American Driving Society
Check other officiating sites to check their rules in detail. Welcome to the world of Driving!