"Is there ANYTHING I can do to influence a Pokemon's moveset?"
When a Pokemon evolves, its quick and charge move are re-rolled according to unknown odds. Conventional wisdom has settled on the idea that the moves are chosen randomly from those available to that Pokemon species. Unfortunately, no study has seriously examined evolution moveset factors, and due to a lack of this data, myths and rumors have perpetuated.
Fortunately, the Silph Research group has taken a look!
When a Pokemon evolves, its quick and charge move are re-rolled according to unknown odds. Silph researchers began recording various attributes of their Pokemon before evolution, including their moves, appraisals, STARDUST
, and their evolved movesets. Over 10,000 evolutions were captured over the course of the study.