Ionic compound are definitely more solubile in polar solvents like water. This is true because since polar molecules like water have a paositive and negative end and this helps to pull ionic compounds apart. This process is called solvatioon.
The second part of your statement can be made true. It is more accurate to say that nonpolar molecules will dissolve in nonpolar molecules and polar molecules will dissolve in ploar molecules. So isoprpinol (which I think is slightly polar, I am pretty sure about tthis but I don't want to go against your teacher or anything) will dissolve in water (which is also polar). Benzine is non polar and will dissolve in vegetable oil which is also nonpolar. The simple reason is that we have this wonderful rule in chemistry called "like dissolves like"
, two things that are alike will dissolve in one another.
Hope this helps, Cheers