The first question to ask is "are you looking to find a primitive root (that is, a value $g$ such that $g^x \bmod p$ takes on all possible values in $\mathbbZ_p^*$), or are you looking to find a generator to the subgroup of order $q$?
The first question to ask is "are you looking to find a primitive root (that is, a value $g$ such that $g^x \bmod p$ takes on all possible values in $\mathbbZ_p^*$), or are you looking to find a generator to the subgroup of order $q$?