Supplies: Brushes, Tack, Water Bowls, Bedding, and Feed Accessories

Of course you will need supplies for your horse. We will start with brushes.
In order to brush the way that I do, you will need:

Dandy Brush
Body Brush
Rubber Curry Comb
Metal Curry Comb
Soft Body Brush
Hoof Pick
Face Brush
Mane & Tail Comb
Sponges

The only things that are absolutely necessary:

Dandy Brush
Body Brush
Hoof Pick

You will also need tack. Choosing the correct ones is described in "Tack:"

Saddle
Bridle/Hackamore
Halter
6 ft. Lead Line

You'll need supplies to care for your tack:

Sponges
Saddle Soap

You'll also need water bowls & food accessories:

1 water bowl for each stall; at least 1 very large water bowl for each pasture
Metal food bin
Grain (this is preferred to sweet feed, oats, etc.)
Hay

You'll want to make the stall quite comfortable:

Straw, sawdust, wood chips, shredded (unprinted) paper, etc.
Rubber mats (optional)
Apple picker or pitchfork
Wheelbarrow or large bucket

Once you get these accessories, you are well on your way to being able to own a horse. And of course there are luxeries and enjoyable things along the way; such as blankets or fly nets, or fly spray even. But these are not necessary in the keeping of a horse, and therefore, you do not need them.