The reason there are all sorts of club and membership options is that the question is unanswerable. We all want something different.
Is a low cost private club possible? Of course it is, if you live in the right place or are willing to travel some to get there. There is something out there for nearly everyone. While a metropolitan citizen has it more difficult to find something reasonable, we in mid to small town America still have options.
Jason, if you want to know if it is possible for a person with little disposable income, or few financial assets, probably only in rare circumstances like a semi-private Wild Horse sort of deal.
I have the perfect set up at my muni. Unlimitted golf for $1135, I get to meet plenty of new players, yet play with my regular circle of buddies 2-4X a week. Men's club, plenty of weekend tournaments, a county open, steak frys, corn roasts, card games, etc. We have a very good quality new clubhouse with a restaurant concessionaire that provides a fine menu, open to the public, yet we never have to wait to be seated, fine veranda for sippin or dining outside, and good service. All that, yet we don't pay per meal and drinks as we go as much as most local private minimum charges, and at about 1/3rd the yearly golf dues. But that is what I like, not what others might like.
Now, saying all that, I would personally be willing to pay about 10-20K initiation (if it had resale or buy back when you leave, etc.) and about 1500-3000 a year if the club was golf only focused on a decent design (no need lush and green) and a reasonable (not fancy) F&B service. But is that low cost? Depends... on your financial comfort zone.
I do think it reveals something about our tastes in the question posed above. Pine Valley at a very reasonable cost, but play alone or with the same disagreeable idiots every time, or low cost semi-private with great playing companions, like Wild Horse or my deal here at Brown County. I'll take the Wild Horse or the county deal every time.