Ok so I've discussed this to some extent in two non-threadmarked posts, so might as well get this one of my chest. (The education post is still coming)
In the early days of Florida society, like in Britain, Canada, or Australia, the only "formal" sport to be played is cricket. As in the West Indies, the sport was not only the preserve of the white plantation-owning class, but it also rapidly grew in popularity among the enslaved population, not least of which because enslaved persons who can Throw A Ball Real Good are often to find themselves on their plantation owner's team, and therefore not being worked as hard, or as long, getting some travel perks and fed better.
Cricket was popular for gambling, which was widespread among the "leisured" class who have the privilege of owning large estates without having to be often engaged in physical labour on them. Card games were fashionable for gambling, and races of various kinds. The 1830s brought a variety of football codes, still not quite differentiated between rugby and football. It also brought the end of slavery, and the diversification of the formerly plantation-dominated economy.
With access to the southern US agricultural economy, raising of cattle and horses for export would increase from this time. These exports would halt entirely during the American Civil War; but they would boom in the years following, as the south had been devastated and the need for animals vastly outstripped domestic supply.
So, possibly before even the Kentucky Derby is first run (in 1872), we see the emergence of Florida Derby, which would remain an important part of the St. Augustine social calendar into the 21st century, and in the second half of the twentieth century, increasingly became seen as the preeminent upscale fashion event for women of colour in the Americas.
The first codified football rules were written in Britain in the 1850s through 1870s, as the old boys from various public schools (meaning, in North America, private schools) wrote laws that would allow them to play against each other at University. This process was mostly completed by 1871, with Football and Rugby being strongly differentiated to observers at them time and recognisable to modern observers. In England, this was followed by the first FA Cup season in 1871-72.
The first football Cup outside of the Home Nations IOTL was the Dominion FA Cup (in Canada), first played in 1877. Florida's started only a few seasons after. After the Football League was launched with 12 professional clubs in the Northwest of England in 1888-89, it didn't take long for Florida to follow, although the League, based in and around St. Augustine initially, would begin as an amateur league and remain semi-professional decades, even as the geographical scope of the league expanded and the quality of play improved.
Similar to the process that happened contemporaneously with football, A Montreal dentist had similarly codified the traditional Haudenosaunee (Iroquois) game of tewa'araton, calling it by the French name for the stick used, La Crosse. It's position as an indigenous game led to an explosion in popularity after Canadian confederation, and by the 1880s Lacrosse was the most popular spectator sport in Canada, and had become quite popular in the Northeastern USA at the collegiate level as well. Lacrosse clubs were formed in Manchester, England and Melbourne, Australia by 1876. Florida, with a substantial Canadian expatriate population, is unlikely to escape this trend and in fact probably sees a Lacrosse club formed earlier than 1876. Because of its proximity to the East Coast heartland of the Sport, and because the indigenous people of North Florida play a similar game, Lacrosse would develop a level of popularity in Florida which was greater than that in England or Australia, and prior to the outbreak of World War I, would have been one of the major spectator sports in the country.
The end of the American Civil War brought about a rise in the popularity of baseball throughout the USA, as well as an rapid increase in the number of American tourists and investors in Florida, which contributed to its increasing popularity around this time, as well. However, the possibility of joining cross-border leagues for Floridian teams was eliminated by the introduction of racial segregation in pro baseball in the USA during the 1880s and 1890s. From this time, because of Florida's small population and lack of formal segregation, Floridian baseball teams would compete in the various leagues at the time which were created to for teams featuring non-white athletes (and crowds).
American Football gradually developed out of Rugby Union, after Harvard were first exposed during a match against McGill (the legend goes that the Harvard Football Club arranged a match against the McGill Football Club, and when McGill arrived in Harvard with 15 men and an oval ball, they had to adapt to the smaller field of the Harvard common, and reduce the number of men to 11 as Harvard was actually a football (soccer) team. This is supported by the fact that the modern NFL field is 120 yards (including end zones) by 53 yards - the exact dimensions of Harvard common, and significantly shorter and narrower than a CFL field).
During the earliest period, from 1869-1882 inclusive, the sport was largely rugby union, but rules introduced by Walter Camp from 1883 marked a turning point for the sport, as "touchdowns" became more valued than goals, "down-and-distance" requirements replaced scrums, and eventually the forward pass was introduced. Meanwhile, the sport spread from its Ivy League heartland. The first match played in the south was in Virginia in 1873. A university in Kentucky organized a team in 1880. By 1888, it was played in North Carolina, 1890 in Tenneessee, and by 1894 a Southern Collegiate Athletic Association was formed including teams from Alabama and Georgia. Again, however, due to the segregated nature of these American universities, who were also substantially larger than their Floridian equivalents, the move toward adaption of "American Rugby Football" is significantly muted in Florida by comparison with Canada, where a hybrid version of Rugby-Gridiron became one of the country's dominant sports in the early decades of the twentieth century.
Sport was, by the turn of the century, often divided by class, location or ethnicity, with American sports most popular in the areas along the border, rugby and lacrosse the domain of the universities, horse racing predominant amongst the upper classes, and football (soccer) gaining in popularity in the industrializing new towns that were springing up in Central Florida and around Tampa Bay. This trend would be exacerbated after the turn of the century with the influx of European migrants. Cricket, although centered at the St. Augustine Cricket Ground, enjoyed a level of popularity everywhere and amongst every class and race (with the notable exception of recent European immigrants) that allowed it to remain the "National Game" long after its popularity was eclipsed. (Although as of 1914, it's still the most popular sport in the country).