Is it possible to register a trademark in my state?
Yes, unlike patents, which are just federal, you can get state trademarks as well as a federal trademark, and I’ve done that on occasion. It depends on one reason to do that perhaps is if you think you’re going to be involved in a lot of litigation, the state trademark conjoined with a federal trademark allows you to have a choice of courts. Do you want to be in federal court or do you want to be in state court?
If you’re just going to have a hamburger business in Florida, and you never care about going to Georgia or Alabama or anywhere, well, just get a state trademark, but you qualify for a federal so my advice would be get the federal.