What general rule can be followed when choosing a type of solvent to dissolve a particular solid?

the polarity of the solute or the solvent.

for example:

oil will not mix with water because oil molecules are nonpolar however water moleculses are polar. so, they will not mix with each other.

when we put sodium chloride in water, sodium chloride will be easily dissoved. because both sodium chloride and water are polar.

in other case, if we put sodium chloride and hexane together. sodium chloride will not dissove in hexane, because hexane is a nonpolar solvent.

finally, if we try to mix hexane and bromine together, they will mix uniformly. because both hexane and bromine are nonpolar. (note: most diatomic molecules are nonpolar, such as hydrogen gas, oxygen gas, chlorine gas, etc.)

so just remember, nonpolar and nonpolar will dissovle each other. and polar and polar will dissolve each other.