Evan, Scot, and Kevin have a couple of hats each that you might see in pictures. Evan's 3 season and high country hat is a brown Beaver Brand 3.25" brim fur felt western hat with a montana peak. Beaver Brand has been out of business for a number of years, but that doesn't really matter because it's not a hat you could have bought off the shelf. The only thing "off the shelf" about it is the brim was already 3.25" and it was brown. Scot can be seen wearing either a silverbelly Resistol with a 4" brim and cattleman crown or a bone Stetson with a 4.5" brim and a montana peak. Kevin wears an RCC 3.5" brim with a 4" crown. In the summer time, Evan wears a Rodeo King Bangora and Scot wears a palm leaf. Palm leafs are considerably hotter than straw but very comfortable. Kevin's summer hat is an Ariat Indiana bangora with 3.25" brim and 4" crown. Both of Kevin's hats have a teardrop crown on them.
To get the hat of your dreams, you're going to need to find a decent western shop that knows how to work on hats. The higher the number of "X's", the more fur content there is. In general, the higher the fur content the better the hat. Evan's hat is a 5x, but there's a lot of variation between brands and periods as far as what a specific X count really means in terms of fur felt percentage. Resistol and Stetson are good established brands that often have models available in a brown color.
From there, you want to figure brim size. A 3.25" brim like on Evan's is considered short for a western hat but it works well with a pack and in a vehicle. Depending on brim shape, anything up to a 3.75" can be worn successfully in a vehicle. A shop that knows how to work on hats can cut a fur felt brim down to whatever width you want. Straw and palm leaf hats can't have their brims cut down.
Next is crown shape. The crown you most often see in the field on Evan and Scot is a montana peak (mistakenly called a Gus ever since the Lonesome Dove miniseries came out. Ironically, the character Gus probably never would have worn a montana peak because it was a northern plains style, not a Texas one). Shaping fur felt hats yourself isn't particularly hard and even hats that have been professionally shaped usually get a little bit of a workover by Evan or Scot. Straw hats are doggone near a one shot and you're done proposition. If you can start with an "open crown" (not ever shaped before), you'll get better results more easily. If it's already got a different crown shape, you can reshape a fur felt. Straw, not so much. Get a pan of water boiling on the stove and use the steam to soften the hat and shape it to your preference. If you want to get a hat professionally blocked and shaped, we can recommend this hattier: https://tattonbaird.com/ There are a variety of crown styles. Evan's good fur felt (a 6x buckskin Beaver Brand) and his summer hat (Rodeo King Bangora) both are shaped into a Southwestern Vaquero inspired crown -- a conical telescope that rises front to back with a slight pinch at the front.
Another small detail that Evan and Scot like on their hats is vents. These are the little eyelet holes in the crown that help with airflow. Finally, they add eyelets for stampede straps. When it gets windy, you'll want one if your hat isn't pretty tight.
There's your start... have an enjoyable trip down the western hat rabbit hole.