Chinese/Japanese/Korean

I’m looking for some advice from anyone who might have some familiarity with these three particular languages. Which of these would you regard as the best “gateway” language? In other words, which of these three would give the greatest advantage in studying the other two, should one decide to do so? I know the grammars of Japanese and Korean are similar, and there is borrowing of Chinese characters and vocabulary among these two also.

I ask this mainly out of curiosity, as I have no plans to learn either of these three for a while yet. The interest factor for me is more or less the same for all three, as I find them all to be fascinating in and of themselves.

I would start with Chinese as a gateway, since it is the source of so much of the vocabulary, and of the culture. I would do Korean last, since it does not use characters, even though it uses the Chinese vocabulary, pronounced as if the characters were used.

But the main motivation should be your interest in the language for other reasons.