Step 1: Concept Arrhenius theory states that an acid produces $H^{+}$ ions and a base produces $OH^{-}$ ions in aqueous solution.
Step 2: Meaning We look for a substance that directly dissociates to release hydroxide ions ($OH^{-}$).
Step 3: Analysis $NaOH$ dissociates in water as: $NaOH \to Na^{+} + OH^{-}$, thus satisfying the definition. $CaO$ and $NH_{3}$ are Lewis or Brønsted bases but not direct Arrhenius bases until they react with water.
Step 4: Conclusion $NaOH$ is the classic Arrhenius base.
Final Answer: (C)