I bought a soft-sided tote for all my grooming stuff. I actually don't like it because the inner lining is black, which makes it hard to see what's inside, especially in the barn. I might cut out all the dividers, which should help. I don't like plastic totes either so I'll have to think of something.
Anyway, in my kit I just have the basics.
Grooming mitt (which I mainly use on my dog anyway)
Hoof pick with bristled side
Dandy brush - natural bristles
Body brush - natural bristles
Face brush - natural bristles
I think that's it. Lots of tack shops sell complete grooming kits that you can either purchase whole or just get use to get an idea of what you want to buy for your own kit. Basically I just stood in the grooming supplies section and chose one of everything.