Bristle brush (sometimes from the dollar store.)
Plastic curry (for winter fur)
Rubber curry (for baths)
Maybe a face brush... meh, maybe LOL.
Coconut oil for monthly hair treatments, and maybe some shampoo and conditioner for the oddball bath that may be needed.
Plastic hoof pick with a brush on the end.
HATE combs because of all the hair that get's pulled out. My "grooming" kit is nice and simple and kept in whatever container I have handy at the moment