Money will be hard at first their is no way that the government will use old U.S. greenbacks or accept them as a legitimate tender as they are lying around everywhere that make controlling inflation impossible so a new currency will have to be made in it's place.
A good way to get it into circulation would be make a market of sorts around project purity and demand that any transaction made in the market by visitors on their way to get fresh water must be paid for using this new currency which can be exchanged for caps and also pay the new government employees in this currency as well further spreading.
As for drugs and guns I don't see them being as much of a problem as the Enclave technically have the second amendment and beyond fat-mans I don't see them rigorously trying to promote weapons confiscation in a society that has depended upon them for over two-hundred years