The western saddle needs to be a reallly light one (not color, i mean weight). And a high cantle is perfect.
For the blanket, most people use a neoprene one. But make sure the one you use is think for padding, and VERY breathable. Don't use a cheap one.
Snaffle bits are fine, a lot of people use Wonder Bits, or hackamores, but if your horse is used to a snaffle and is controlable in a snaffle, then i say stick with it.
In rodeos, most of the time the girls wear chaps, but it's not necessary.
But you will need western boots, jeans, a button up western long sleeve shirt, and if by any chance this is an NBHA show, you'll need a western hat or helmet.
Some people wear shin protectors. But it's really only necessary if your horse hits the barrels a lot.
If your horse is lazy, you might want an over-under, or ball spurs.
Also, your horse will need boots. Professional Choice SMB seem to be the most popular.
Most people braid their horse's mane because the mane often gets all tangled up your hands when you're turning. You can braid the tail too so he doesn't step on it, but it's not necessary.
Oh, and most importantly, always, always, ALWAYS, remember to bring your enthusiasm.
:)
sorry it's so long.