Hey, welcome! =)
Have you seen the new Top Down Shooter Movement tutorial? It's an example of how to get the side to side movement and such. Generally, simple movement is super easy. Get the axis inputs, then feed that data into another action that can move/push the ship around.
For the movement, you can use the Itween actions to move things on a spline/path, they're pretty powerful. For projectiles its just a matter of spawning a prefab that moves in a forward direction when its spawn and does something on a collision. We'll have a new tutorial explaining projectiles/damage/health in the TDS series soon, like this week.