You have to consider the nature of the reaciton (SN1, SN2, E1, E2) and the structure of the reactant. I don't remember the specific rules, but know the answer lies in what solvent is appropriate for the particular reaction.
The biggest difference in solvents that will have an effect on reactions is whether the solvent is protic or aprotic. SN2 reactions prefer aprotic solvents, for instance, while SN1's prefer protic. Usually, a multiple choice question will have one of one type of solvent and four of the other type.
Common protic solvents are alcohols, ammonia, various acids....
Common aprotic solvents are acetone, dimethyl sulfoxide, dimethylformamide...
also remember like dissolves like. if its a nonpolar solute look for nonpolar solvent(lots of hydrocarbons).and if it's polar look for polar solvent(OH groups and charged molecules).
I wrote a post in the subforum about the four substitution and elimination mechanisms that you may find helpful, particularly the part about solvent. It's in the organic chem explanations thread. Also, there is a post in the gen chem explanations thread about polar protic versus polar aprotic and how to determine which is which.