You can get your first free armor at the New Mine. Starting from the New Camp, walk to the mountains, keeping Cord and the lake on your right. After the scavengers, the two molerats and the wolf, you will reach the mine of the New Camp, guarded by the mercenaries.
Climb down and speak with Swiney, the boss of the mine, he is usually smoking his weed joint. He will give you some miner clothing for free.