Depending on the level of showing, you may not even need to braid. Especially if you're doing equitation, that is on you not the horse. Also, she is a Mustang! Its their "breed standard" to have a thick mane and tail. You could french braid it (And show off her brand if she has one) or diamond braid it. You could even scallop braid it if you have that much time. And just a regular old hunter tail braid will work for the tail. Its awesome that its so thick but remember to take very small pieces or else it wont look as great. You may also want "bang" the bottom but that's up to you: you trim the long hairs and make it more flat across the bottom. It makes it neater and look more full. But don't hack away, just a little snip snip is all you need :)
"Don't turn you disabilities into a crutch, turn them into legs and run with them"