I do not have the time to research making a gun legal to own when I have no idea of it's origin.
Only in a place like New York would that be a concern. I could not prove the provenance of most of the guns I own. To get a license to carry, you don't even have to own a gun. You can rent one where you take the course. You can rent guns before the course and fire different guns to determine which gun you feel most comfortable with. In most states, unless the gun has been stolen and is in the NCIC data base, it's presumed to be legal. To me, "making it legal" should be of no concern.
The way right to carry has evolved in Texas, a CHL is almost an impediment, since someone without a CHL has almost as much leeway to carry as soneone licensed, while certain actions by a license-holder can get hin/her in big trouble.
It's interesting that Vermont, that very liberal state near you, allows its citizens to carry without a license. Shows that they trust their citizens, while New York, New Jersey and some others fear their citizens or something.