In Alabama, I can buy a standard firearm, meaning not fully automatic, suppressed and etc., from a private party without an owner's permit or an NICS check.
A firearm transferred in from another State's seller/owner has to be processed through an FFL and I pay the FFL a nominal fee and he/she processes the NICS check on me. The transfer from my FFL to me does not require anything from me other than my driver's license, no owner's permit requried, and the completion of the NICS form. Normally takes about ten minutes.
If I purchase a firearm from a guns store, then the store processes the NICS and it is typically free. The paperwork takes ten to fifteen minutes. Just my drivers license and no owner's permit needed.
If I choose to have a concealed carry permit I go to my County's Sheriff's office to obtain a concealed weapon's carry permit. This is to carry a firearm concealed in public either on your person or in a vehicle/boat while off private property. The sheriff's office does do a background check on you and it takes about 15 minutes and an annual fee varying in cost from County to County. My County is $25.00, but it is reduced to $20.00 if you are a Senior Citizen. You can do the renewals by mail. Where I live, there are no local police. The 660 plus sq. mile area is covered by the Sherrif's Department. It is a small force. As you can imagine, the nearest Deputy can be a significant distance away in the event of an emergency call.