Which is more appropriate regarding Bernoulli's principle
- fast moving air causes low pressure or
- lower pressure causes fast moving air.
Low pressure in itself does not create any flow, as the pressure is the same everywhere. Bernoulli's principle should always be applied between two point along a streamline. When doing this, you will find that only the pressure difference between to points play a role.
Then, it comes down to the specific problem your are studying. Sometimes you will have information about velocities, sometimes about the pressure or the height. There is now general statement possible.
Neither of your two statements have any validity to them and are therefore not applicable to understanding Bernoulli's principle, let alone more appropriate than the other. Pressure is a relative quantity that has little meaning by itself. Changes in pressure have meaning and can cause fluid motion. For situations where irrotational flow is a valid assumption, the primary driving force behind fluid motion is the need to respond to boundary surface geometry.
Definitely the second, assuming that what you meant to say was "Relatively low pressure causes fast moving air." Bernhard is absolutely correct on this point, in that really it's the pressure gradient, not the pressure itself which causes local accelerations in the flow. The language I am using is very deliberate, suggesting that the pressure gradient causes the flow accelerations and not the other way round. After all, Newton's Second Law tells us what an object will do when a net force is applied to it, not what forces will be generated when it just begins to move apropos of nothing. Forces cause accelerations, and so analogously the pressure gradients are what cause the local flow accelerations (although the phenomena are dynamically coupled).