I've been a member of Pony Club for about 4.5 years and the type of braiding kit depends on the type of braiding you will be doing. If you're looking for a braiding kit for pony club testing reasons, you wont loose marks for not having a braiding kit within your groom box, but you will need a metal pulling comb in your groom kit.
But if you're planning on just rolling your braids and either taping them at the top or just putting an elastic around them, you'll need Elastics [the colour of your horses mane or as close as possible] and you can get a back of like 500 elastics for $2.00 at your average tack store. If you're going to be plating a mane 'pony club' style, you'll need elastics, a proper sewing needle for manes, and the proper string. All of this can [or should be] found at your local feed store. If you have anymore questions about Pony Club just PM me!