Why did the country club play such a crucial role in the sporting practices of the super-rich?
What role did the amusement park play for the working class?
Did the middle class have its own special recreational place(s)?
I think that that some of the sports that the "super rich" enjoyed could only be done so in a country club setting. For example, sports like polo and equestrian activities required the country club backdrop as well as wide spaces. Horses are not going to be able to hang too well in the urban planned city streets. Golf is another activity that required a large amount of space and one where the country club setting worked very well. These activities were ones where space, maintenance of grounds, as well as equipment cost and upkeep were very good fits for the country club crowd. Middle class people did not really enjoy country clubs, as much. Public parks and even congregating in the streets to play games such as stickball or other elements that did not require much in way of equipment and space. The reality was that the "super rich" were able to partake in experiences that the middle class could not be enjoy due to resources and their allocation.
You only get to ask one question, so I'll deal with the first one. In a world where connections are everything, the country club was the premier place for the ultra-rich to meet with other ultra-rich people in a more casual yet selective environment. Country clubs were for the more elite sports, such as polo or golf, which weren't as accessible to the average guy.
For men, the club offered opportunities for informal business dealings and networking. In other words, the only other golfers on the course were also the business moguls, the elite, the movers and shakers, those who could make million-dollar deals with a handshake at the 13th hole. The exclusive nature of country clubs (many of which were segregated by more than money) not want to be bothered by inferiors. There was a time when being asked to join a golf foursome at "the club" was a golden ticket--an opportunity to rub shoulders with potential financial backers and investors.
For women, the country club was a place to "see and be seen." Women were not generally there to conduct business; however, they were certainly there to solidify their husbands' social standing. Their part, if you will, was to promote the family business by maintaining an elegant social presence and gathering any helpful information for their husbands. Though they didn't talk business and made no hand-shake deals while at the club, there were undoubtedly many "suggestions" made to their husbands over pillow-talk after a day at the club.
Entrance into such country clubs was outrageously expensive and exclusive. In other words, one not only had to have money but be among the desirables--and "old money" was definitely preferable to "new money." Members were often recommended, but no one got in without a vote. The sport (golf or polo or whatever) was secondary to to the networking. Country clubs were the playgrounds of the elite.