You are right that this part of the sentence is trying to tell you which generating set to use to construct the Cayley graph of the group.
It's telling you: use "the standard one". In this case, "standard" is not mathematical terminology, but just means that we do the most obvious thing.
What the most obvious thing is might not necessarily be all that obvious. In this case, I would say that
- The standard generating set of a cyclic group is a single element generating the whole group.
- The standard generating set of the semidirect product of two groups is the union of the elements generating each group (viewed as subgroups of the semidirect product).
So in this case, the generating set you are asked to use consists of two elements: an element generating the first cyclic group, and an element generating the second.