I practiced tax law for 25+ years. I see advantages of the 501(c)(7) "Social Club", but if it were me, I'd seriously look at the LLC route. You may have read where Pa LLC's have a $500 or so annual fee for each member of the LLC, BUT that is just for "Professional LLC's". You know....Licensed professionals like Attorneys, CPA's, Dentist etc. For a hunting club that annual fee doesn't apply.
And just the upfront disclaimer, consult with a tax attorney or attorney and CPA who knows the tax laws. Don't print this out and say...."This guy said". I've been out of the business for many years....some things change....some don't.
An LLC is taxed as a "Disregarded Entity" which means if the LLC has no sources of taxable income (royalties, timber, etc) then no tax return needs filed. Member contributions are not taxable income. Should the entity have taxable income, the "default" for more than one member is a Partnership Return, form 1065. You really don't need a professional to file the 1065...if needed. Especially if it's just royalties and\or timber.
Remember, nobody "owns" a 501(c) organization. The 501(c) has bylaws that control it's operation....and it's controlled by the Directors that are appointed. The 501(c) would work when\if there is no buy-out issues to contend with. In other words, if a member put in $5,000 for a contribution, he owns nothing to sell at a future date. Also, as a side note, should the organization want to change the bylaws, a copy of the changes must be submitted to the IRS in the year any changes were done.
"Buy-Outs" with LLC's can be controlled via buy-sell agreements. With LLC's each member owns "membership interest" similar to corporate shares....and these same membership interest can be voting and non-voting. The Operation Agreement controls this. A buy-sell agreement can simply state if you put in $5-K, then if you ever want out you can only get $5-K and it can address a time period for the buy out to be paid. (Thus averting the need to cough up cash right away) Buy sells can also control the "who" the owner can sell or transfer their interest to. Agreements can be stated so that existing members have the first right of refusal to buy....so one guy can't transfer his interest to...say his soon to be ex-wife etc.
Is it more complex than just buying a camp with a bunch of guys? Yes...a bit more. OTOH when down the road members pass away, get a divorce, have children who all receive a chunk of Dad's share of the real-estate in the camp....then decide to come up with 25 of their friends to party during hunting season.....things can get sticky.
So....some complex now can save a lot of grief and aggravation down the road. And can also provide the members with an easy way to control who owns what....and who can use it when.
FWIW