Which is conductive in water and which is soluble in water when it comes to ionic and covalent bonds?

Ok.
All polar molecules will dissolve in H2O, regardless of their bonds.  for example, NaCl dissolves in water and is ionic (salt), but so does C6H12O6 which is covalent (sugar).  However, when the sugar dissolves the water breaks off molecules from the solid, and they are dissolved as is.  But when salt dissolves, it ionizes into Na+ and Cl-.  because of this, it will conduct electricity while the neutral charged sugar will not.  hope that answers your question.  In summation
All polar molecules dissolve.
polar covalents dissolve but do not ionize to conduct electricity
polar ionics ionize to form electrolytes, and will conduct in solution.