Even some of the "parced down" lists here look pretty extensive to me.
1 curry brush
1 hard/dandy brush
1 mane/tail brush (just an old hairbrush)
1 hoof pick
... all stored in an old feed bucket
1 rope halter
1 lead rope
1 fly mask
1 fly spray
1 western saddle
1 western saddle pad (although I did for awhile borrow one from my coach -- it was built up and I needed it while my horse was still building muscle)
My mare thrives on plain old alfalfa and bermuda hay.
As for emergency funds, everyone does it differently and there are so many things that can come up.
My horse cut her leg open and all that had to be done was clean it out stitch it up with localized sedation but it was over $1,000. We chose to insure my horse for medical costs (up to $6,000 I think) and you might want to look into it but there are many reasons a horse can't be insured.
A horse at my barn had cancer in his eye and it had to be removed, now he has a partially paralyzed face and they don't even know why (could be that the cancer spread, could be that the surgery to remove his eye they nicked a nerve, anything)... I can't even imagine the vet bills
"I don't think he ever gave a thought to other people's opinions, which was just as well because they were often unkind."
-- James Herriot, All Creatures Great and Small