OK so western pleasure, horsemanship (basically the equivalent of equitation), trail and reining you can probably get by on the same outfit for. You'll need:
Chaps (probably a neutral color to start out with I.e. Black tan or brown)
Pants that match the color of your chaps preferably without back pockets.
Boots that match chaps and pants
Belt (most of the blingy type belts come with buckles that are large enough to work, but you can also buy a round silver buckle)
Hat (preferably same color as chaps but not totally necessary depending on your shirt).
If you get a tunic top you can get by with wearing it un-tucked with just your pants and hat and belt for halter and showmanship.
There are a variety of different style tops to choose from. Just like with regular fashion things go in and out of style. My advice you be to check out hobby horse. They have some outfits put together that should give you an idea of what to start looking for. Or just do a google search of imags from World or Congress of the disciplines that you're looking to get into. She what the top competitors are wearing and go from there.
Blah, tried to keep it brief. I hope that helps.