I'm going to go against the crowd and advocate for a sole proprietor owned club. For profit.
It's kind of interesting to me that this group, who is typically anti government, thinks the most important thing is to make sure YOUR club has a good government. There is no such thing. They may start off great, but eventually, they all go to shit.
You are a gun guy. You have been involved with gun clubs. Set rules and policies that you know most shooters will want and implement them.
Sure, sell memberships, but allow people to come and pay to play as well. Maybe keep members areas separate from non members, so that you don't have to worry about getting shot or muzzle swept by noobs.
And yes, sell stuff. Sell ammo, targets, eyes and ears, and maybe eventually firearms etc. Shooters will spend money. How many times have you driven to the range only to realize, "oh shit, I left my box of 357 ammo at home!" or just needed something that you didn't bring with you?
Lets say a club has 200 members as you have suggested. At $150 per membership, that is $30k per year. After taxes and insurance, there is literally nothing left, if that is even enough.
Nope, I would suggest you need to generate enough revenue to maintain a decent facility or people will quickly loose interest.
Small membership + reasonable membership costs = you are spending YOUR money to maintain a gun range. That will get old quick.
You mentioned a long dirt road leading up to the club. It has to be maintained, snow has to be plowed. It can't be accessible for 4 months a year to only people with 4wd vehicles
My perfect club would be a mix of Harvard meets American Firearms School. I like the idea of a pro shop. I would like a clean and well maintained facility. It would be great to be able to get a hot cup of coffee or an ice cold gatorade, a place to meet friends.
We are all shooters here, so everyone is going to say " It needs to have a 600yard rifle range!" Maintaining that range is a bitch. First time I shot at 300 yards at Ames, I walked down and set my targets, and walked back, then spent 10 minutes pulling the ticks off my legs, and the grass wasn't even that tall.
You have to cater to pistol shooters first, because that is what most people shoot, especially new gun owners. Newbie buys a gun for personal protection, he wants to take it out and shoot it. Joining a club takes time and is not easy. But he will gladly pay $25 to shoot it. Then he will tell a buddy, and they will go together, and he will probably shoot it one more time, declare himself an expert shooter, and hardly ever shoot again.
My perfect range looks like Hickok45's. Tons of steel, and can shoot rifle or pistol, but can also set up paper targets.