Hats are the cherry on an ice cream sundae (you!) and mean a lot to the western folks. Kind of like the $1200 hunter bridle I just saw mentioned in another thread… it’s a prestige thing.
A cattlemen’s crease (kind of basic, symmetrical, like a great little black dress) is always in style, with a 4 1/2"- 5" or so brim for ladies shaped semi-taco-ish these days is a good starting point.
I would suggest that you avoid Boot Barn and their ilk for shaping and take your hat (or buy one) at the larger AQHA/APHA shows from a hat vendor there. The folks in western stores generally cater to dancers or ranchers whereas the hat vendors at shows are in the know for that specific group: show riders. Most of the larger shows will have a hatter there who can advise you.
Be sure to invest in a good hat can and adjust it properly to keep your hat looking good. No part of the hat brim should touch the can (or box if that’s what you’ve got) except right around the crown where it fits into or over a ring kind of shaped like your head. Don’t store your hats in the horse trailer, bring them in the house- they can get too hot and humid in the trailer and heat warp to look like tortilla chips.
Have your show hat shaper educate you about what they are doing, and memorize how the hat looks when it’s freshly-shaped. It may need a tuneup a couple times a year, especially if it’s not a very high quality felt that won’t hold a shape so well. Felt hats are rated by X’s but any manufacturer can claim any quality of X’s… a 10X in one brand may be equivalent to a 5X in another brand. There are no real felt hat quality standards but generally more money is required for a fur felt hat, made from things like beaver, chinchilla etc fibers rather than wool. Wool fibers don’t felt together as tight as fur felt fibers so wool hats often get droopy fast and have a rougher surface.
There are major supply chain issues with hat bodies (the unshaped felt cones that get turned into hats) as well as the very skilled labor needed to craft a fine hat these days, so if you are buying a new hat, expect sticker shock. A nice 15-20X hat in most brands is going to be something like a $500-$800 purchase. But like other quality horse gear, you generally get what you pay for and better equipment should give years of service.
A note about buying western felts online: just because you buy a good hat from a reputable seller is no guarantee that is will arrive looking good after a cross-country trip knocked around in a box. Plan to have it checked out by that great hatter you see at shows, or save yourself a lot of freight cost and buy from them in person. Shipping a hat has become crazy expensive (it’s basically shipping a box of air with a fragile thing suspended in the middle of it) and even the finest hats sometimes get very abused in shipping.
Or… just wear your helmet and show off your horse and your own skills with your head well-protected! It’s becoming much more common the see safety gear in western events.
Good luck and have fun!