This is perhaps a naive question, but why do we write down the Lagrangian

$$\mathcal{L}=\frac{1}{2}\eta^{\mu\nu}\partial_{\mu}\phi\partial_{\nu}\phi - \frac{1}{2}m^2\phi^2$$

as the simplest Lagrangian for a real scalar field? This is by no means obvious to me! After all it gives rise to a kinetic energy term (fine), some specific unmotivated potential energy (less fine) and a gradient energy (even less obvious).

Is there some principle by which we know to study this Lagrangian? Is it just that $\mathcal{L}$ gives rise to a nice equation (the Klein-Gordon equation), which we can interpret in an appealing way? This reason seems somehow hollow!

I've heard people mention causality as a motivation, but I can't see how that ties in. Could someone provide me with some intuition?

Many thanks in advance!