After deciding on the control scheme (just switching direction, auto move and auto shooting), it was just a matter of finding an interesting balance. In the end I decided to prioritize trying to destroy as little as possible while surviving the turret attacks.
Code-wise, it's nice to notice the AI for the turret. It tries to be smart and predict your movement patterns. It became too good, which made me add a shield to the player. The shield, on other hand, made the game a bit longer, which allowed me to add a score very strongly biased towards not destroying things.
Visually, we kept the minimalistic color/black/white theme, which I think works great.