While every rider/horse combination may prefer different objects in their grooming kits, the basics needed for every grooming kit are:
Rubber curry comb
Hard brush (rough bristles)
Soft brush (soft bristles)
Mane & Tail brush (You can even use a human hair brush for this)
In addition, I also keep these in my kit:
Shampoo & Conditioner
Oster is known for being a really good brand for already-made grooming kits. I prefer, however, to buy individual brushes & such and combine them to make a grooming kit.