The main Florida background check resource is the Department of Law Enforcement, where you can get copies of someone's criminal history. You do not need any fingerprints for these requests and you can even do a records search through their website if you wish to pay the $24 fee with a credit card. If you need a certified copy for legal reasons, you will have to make your request through the mail. Their website also allows for searches through their sex offender database.
Other Family Sources
Another Florida background check resource is the Department of Health. They will issue copies of marriage or divorce records to the general public for a fee of just $5 to find out more about someone's past married life. If you need them, death records are also open to the public but birth records are confidential unless they are more than 100 years old.