Of the four general types of solids [molecular, ionic, network covalent, metallic], which one[s] are generally soluble in nonpolar solvents?

I'm thinking either molecular or ionic. Are either [or both] correct?

molecular: like dissolves like is the rule of thumb.

You are correct in narrowing down the options to molecular and ionic solids. To determine the solubility of a solid in a nonpolar solvent, we can apply the "like dissolves like" rule of thumb.

Nonpolar solvents, such as hexane and benzene, have a similar nature to molecular substances that are composed of neutral molecules held together by weak intermolecular forces. These molecular solids are typically composed of nonpolar covalent bonds and exhibit low polarity.

In contrast, ionic solids are made up of ions held together by strong electrostatic attractions and do not consist of neutral molecules. Therefore, they are generally not soluble in nonpolar solvents.

So, in this case, your initial intuition is correct. Molecular solids are generally soluble in nonpolar solvents, while ionic solids are not.