Originally, only citizens with a certain amount of wealth were eligible to serve in the Roman army. They were responsible for the upkeep of their own equipment. Polybius records that each of the different types of soldiers had their own equipment made from the same standard materials and with the same standard measurements. More desperate times saw the wealth requirement lowered, and in the aftermath of the Battle of Canne in the Second Punic War, slaves were enrolled and presumably armed by the state. The Second Punic War also saw Scipio getting the Sicilians to supply horses, equipment and pay to men fighting in their stead, but this was not normal practice. Clothing was provided by the government (with production contracted out to citizens). There was weapons production in workshops attached to armies in the field, although I can find no definitive proof of whether soldiers also looked after their own weapons once there was peace or if they merely paid for them. Later, the reforms introduced by Gaius Marius opened up military service to those without any landed property, with the government being fully responsible for their arms.
Like other spoils, some weapons were put up for display in the Temple of Jupiter and others were distributed to soldiers. Rome was known to learn from the militaries of their neighbours and enemies, the most prominent example of this being their adoption of the Spanish sword. In this instance, it is likely that they would have reused captured weapons instead of casting them anew.