If you do not have an LTCH, you can't take your handgun to a range. I don't know about renting.
Also, see here: https://www.indianagunowners.com/fo...ing_a_handgun_without_a_license_official.html
I was told by the police department in my town that as long as to and from the shooting range, your gun is locked and unloaded, in your trunk, you can go to the shooting range. Also this only applys to hand guns, I do not know about long guns.
I also have been told this same thing by a LARGE amount of people how work in the gun industry (shooting ranges, gun shops, etc..) that this is true.