The two most thorough secondary sources on Florida law are both on WestlawNext
While Florida law schools publish many different journals and law reviews, searching just those sources is not a comprehensive way to find information on Florida law.
Individual Florida agencies can be tough to find through search. There is a list of agencies on the state web site.
The Governor's office has its own website, with information about executive orders and judicial appointments.
When learning about the legal system in a new state, often the best place to start is the state constitution. Florida, for instance, has had several Constitutions, and the current version is more recent, and much longer, than the federal constitutions. Some questions that the federal Constitution leaves to Congress or the President to answer are more explicit at the state level. In addition, a state constitution can guarantee rights that the federal Constitution does not include.
You can usually find a copy of the Constitution at the beginning of a state's annotated code.
The Florida Courts main web site is http://www.flcourts.org/. However, there is also much useful information from the Florida Clerks' website. For court rules, you can check the Florida Bar, but Westlaw or Lexis will likely be better options.
The Florida legislature has a portal for both the House and the Senate. In addition to current legislative information, there is a free copy of the statutes, but it is better to use a paid database if possible, to be certain of the currentness of what you are researching.