The EC rule:
ARTICLE G202 TACK AND EQUIPMENT
6. Reins: entirely leather of any description, buckled, studded or sewn; single rein pelham and pelham converters are only allowed in junior and amateur classes in 3’ (0.90m) or below. In the case of bad weather, at the discretion of the judge, steward and/or competition committee, rubber reins may be allowed.
So which reins can you use?
The most commonly-seen reins in the hunter ring are laced reins. Each side is made of a long piece of leather that has two narrower strips of leather woven through it for grip. They are relatively easy to keep clean and, while they are not as grippy as rubber reins, they are easier to hold on to than plain leather reins.
Braided reins are not as popular as laced reins, but they are made entirely of leather and are allowed in competition. Rather than having a solid piece of leather down the entire length of the rein, braided reins consist of a length of braided narrower strips of leather.
Plain reins are just a solid piece of leather and are generally used as a curb rein because they provide less bulk and allow the rider to feel the difference between the two sets of reins. They are less grippy than the others and so are not generally used as the main reins. Plain leather reins with rubber on the inside for extra grip are not entirely made of leather and are therefore not legal.
Whichever type you choose, the key is for the reins not to stand out. They should be the same colour as the rest of your bridle. Whether you go with a buckle attachment or a stud attachment is your choice, but I find that the stud attachments blend in better and provide a cleaner picture.
Most reins are available in different widths, and because there is no rule about rein width, you should just choose whichever width feels best in your hands.