My name is ***** ***** I am an experienced criminal
The state of Florida will restore a person's gun rights if he has all of his civil rights restored, INCLUDING his gun rights. Civil rights are not automatically restored in Florida. You would need a pardon from the governor to get your rights back. There's a waiting period as well before one could be eligible to apply for a pardon from the Clemency
Board. You are well past that waiting period, however, and you can see just how to try to do this here.
Once all of your state rights rights are restored via a pardon, you should be able to clear a NICs check to purchase and own a firearm.
Pardons are rare but they are free, you can do it for yourself, and you have nothing to lose. In fact, if you have had a clean record since 1979, you'd be a much better candidate for a pardon than many other applicants.
You can read about it and get the forms to fill out here.
The office of Executive Clemency does the screening for the governor. A full pardon would not erase your felony but would be official proof that the highest official in the state believes you are rehabilitated, and the Federal government would accept that and lift their bar to your gun rights.
There are lawyers who specialize in Pardons, expungements
and the restoration of second amendment rights, if you don't feel inclined towards fo-it-yourself lawyering. To find one contact the Florida State Bar Association's Lawyer Referral service, or a commercial legal referral service such as Martindale.com.