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What´s the importance of the normalization of the Kinetic term?

Am I obliged to have the Kinetic term in a canonical normalization (so that ${\cal L}_2$ is "wrong")? If so, what conditions impose this normalization? … In both ${\cal L}_Z$ and ${\cal L}_2$ I messed up with the normalization of the propagator, that means I will get $\langle p | \phi(0) | 0 \rangle = {1\over\sqrt{2}}$ instead of $\langle p | \phi(0) | …
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