I suggest you have most or all of the following in your grooming kit:
BRUSHES
- rubber curry comb
- plastic curry comb
- metal shedding blade (the circular ones are best)
- hard/dandy brush
- soft/body brush
- finishing brush (if you show)
- mane and tail comb/brush (you can also just use the dandy brush)
OTHER TOOLS:
- hoof pick (a MUST)
- sweat scraper
- sponges
- scissors (you never know)
- clippers (these can be cheap if you hardly ever clip your horse, but better quality ones are a good investment)
- detangler (this will save you a LOT of time and energy!)
- shampoo
- fly spray
but, if you just want a little grooming kit and you don't own a horse, you can just get a curry comb (rubber or plastic), a hard brush, soft brush, hoof pick, and mane comb.
good luck and i hope this helps!