We ask about your location here at TFL, because state laws vary widely. For example, in NY, I don't think you can even handle a gun in a gun store without your NY Firearm Owners ID (by whatever name it's called). In some states, there's a roster of acceptable firearms for purchase. In Chattanooga, TN, I don't think you'll run into anything like that.
For a newcomer, getting some training or instruction is really important. Look for an introductory course. We were all beginners at one time or another. It was just further back in ancient history for some of us than for others.
Rentals: As far as I've ever been able to tell, just about every range that rents guns makes you buy their ammo for their rental guns. That's to keep renters from blowing up their nice rental guns by shooting handloads of questionable origin and composition. (Aka "a Ziploc bag of gun show reloads")
Each range will have slightly different procedures. At one near me, I show them ID, sign in, and am assigned a lane. At a second one, they make first-time visitors to the range (whether renting or bringing their own gun) watch a safety video. At a minimum, you can expect to show some ID, fill out some paperwork (which will ask whether you're legally allowed to possess a firearm, among other things), read and acknowledge some safety rules, get eye and ear protection (every range around here provides it for free, but it's not high-quality gear), and pick out the gun(s) you want to shoot. You may have to buy targets, or that may be included in the price.
Call the range in advance and just visit with them about their procedures. I've done it when I wanted to go to a newly-opened range here. You won't be the first person to do so, and you won't be the last.
Good luck and please keep us posted.