Which of these would most likely be a strong electrolyte?
Yes. You are right. Ionic compound are strong electrolytes if they are soluble in water. $\ce{CaF2, BaSO4}$ are ionic compounds, but they are not soluble in water. I would not consider them as strong electrolytes. On the other hand, ionic compounds are a part of the bigger family of the polar compounds. But polar compounds are not always strong electrolytes. $\ce{CO, H2S, HF, H2O}$ are polar, but they are not strong electrolytes.