Just use the weapons with the higher damage. The uniqueness is worthless, just take a look at it for the sale.
If you have two weapons, one with 7 damage and one with 6-8 damage. I normally take the 7 damage, as the damage is constant. The chance for dealing 8 damage is as high as the chance to get a low damage of 6.
Just sell your smaller weapons right a way. Give everyone the best weapons you have. Maybe hold 1-2 in your stock in case you get new dwellers. Everything else which is under your "current weapon standard" can be sold right away to save space in your stocks.