The first issue is to understand the difference between SN1 and SN2 reactions. An SN1 reaction is essentially formation of a carbocation first. Tertiary best, then secondary, and not primary (unless allyl or benzyl). An SN2 reaction is attack first and has a transition state. Is this an SN1 or SN2 reaction?
Generally, the leaving group in either reaction is a weaker base than the nucleophile. If you wished to compare the basicity of an amine, alcohol, and methanesulfonate, you need to look at their acids. A ammonium salt (~11), alcohol (~16), and a methanesulfonic acid (~-3?). Which do you think will form?