A good nucleophile is always a good base, but it is not necessary that a good base is always a good nucleophile. Other factors like bulk of base, steric effects r effects the overall nucleophilicity oif the base. If u use a bulky and strong base, surely E2 product dominates in Sn2 substitutuion. However is u use light strong base, Sn2 product dominates.     

the properties of a good nucleophile : 

1. high electon density on central atom.

2. less sterically hindered.

e.g. OH^- , RO^- 

the properties of a good base: 

high K_b

* A good nucleophile can also be a good base.

* wheather S_N2 takes place or E2 depends on nature of both substrate and reagent(nucleophile), 

first observe substrate- primery , sedcondry or tertiery

then if its primery , see if its hindered or not

if its hindered then surely elimination takes place (nucleophile will not substitute due to steric reasons)

if its not hindered then see if the nucleophile is hinderded or not .

if either of two (substrate or nucleophile) is hindered then E2 takes place , OR Sn2 takes place.

Secondary substrate : elimination will be major if nucleophile is good base

tertiery substrate : elimination.