if you were not told which solvent to use in the recrystallization experiment, how would you determine a suitable recrystallization solvent ?

Answer 1

trial and error

Answer 2

The ideal solvent for recrystallization is one in which the solute has high solubility at high temperature and low solubility at low temperature. You could try to look up solubilities in chemistry handbooks or experiment with different solvents. If you have to do that you might include mixed solvents.
If temperature differences do not produce much difference in solubility, you might have to bring about recrystallization by solvent evaporation. The solute must have high solubility in the solvent.