In terms of opening up historical materials which you might otherwise be unable to read, the highest payoff in terms of span of history, population and volume of materials would likely be Chinese and then Arabic. That said "reading Chinese" and "reading Chinese as was written by scholars in the Tang Dynasty" are different things. . .

More generally there is no "best language". Historians learn languages for two reasons-- to read original source materials, or to read scholarship that may be in a particular modern language. People studying Byzantium often learn to read Russian-- not because the Byzantines spoke Russian, but because so much important scholarship is in that language. Similarly, there's a lot of German language scholarship for the ancient Near East and also Islamic history, not translated, and graduate students will often be required to learn to read one or two modern languages just for this purpose.

/u/amp1212 has already addressed the main points. I'd just add that the answer ultimately depends on your goals. Eventually, there's a good chance you end up able to read quite a few, at least to the extent that you need, but it's almost entirely based on necessity.

What language to learn as an historian depends on the kind of historian you hope to be.

But yeah I also want to stress that Tang era Chinese is the same as Qing era Chinese, although there is plenty of overlap, and you can learn the changes from period to period.

If you're into the near East, I'd say Standard Arabic and Persian would be hugely useful.

I want to expand on this but my phone is ringing so I'll have to come back to this.