Race has no impact on that... well, other than deciding whether you know Guns or Bows at lvl 1.
Hunters can train to Dual-wield at 20, can learn to wear mail at 40.
To learn to use other weapons, you have to pay weapon masters -- these are located in your capital cities (Orgrimmar, Thunderbluff, Undercity). Ask the guards and they will mark the weapon masters on your map.