I am relatively new to firearms and had trouble locating a gun store and range near my home, which is in the Chicagoland area. A helpful site for locating gun ranges nationwide is Where To Shoot. Searching on Google worked well too.
For anyone in the Chicagoland area, I have found that Maxon Shooters Supplies and Indoor Range and Midwest Guns are good places to go shoot or buy a gun. Maxon allows shotguns and rifles, while Midwest only allows handguns and .22 rifles. Both offer handgun rentals, although I believe you need to bring along a 2nd person to rent a handgun (but this 2nd person does not need to have a FOID card or fire the gun).
If you are looking for a trapshooting range, I would recommend the Naperville Sportsman’s Park. It is an (outdoor) trapshooting range that is open to the public, and with reasonable prices. I’ve found the sportsmen here, many of whom are members of the Naperville Sportsman Club, to be great people to shoot with and learn from.
You can also consider purchasing a gun online. Keep in mind that the gun will need to be shipped to a local gun dealer, where you can then pick it up in person, rather than directly to your home. Gun accessories, however, can be shipped right to your home.