In Indiana, all NFA weapons except short barreled shotguns
are legal. An AOW that is a shotgun handgun (a short barreled shotgun without the buttstock) is perfectly legal.
I *think* that one would have to take a virgin shotgun receiver to make that shotgun handgun, as simply cutting down an existing shotgun will always be a SBS, which is illegal here.
For just purchasing a handgun, there is no permit, waiting period, nothing goofy like that. If I want to buy a handgun (or thirty) and I have the funds to do so, I'm taking it home with me in less than 15 minutes. There are also no restrictions of any kind transferring firearms between adult individuals (except maybe if you have reason to know that person is a prohibited person, but getting yourself involved in that would be stupid even if it were legal). No safety checks, registration, or anything like that.
Until recently, a "License to Carry Handgun" was need to transport a handgun (even unloaded, cased, locked, out of reach, whatever) anywhere except from the place of purchase to the person's home or fixed place of business, or back and forth between a place of repair and the person's home or fixed place of business. You technically could not legally transport a handgun to the shooting range without the LTCH.
But that has been fixed now (and I don't know of any
instances that anyone was placed in any legal jeopardy for violating the law as it was written).