I'm so glad you asked!
If you want to do this right, you should become proficient in Greek, Latin, German and French at the least, because translations of philosophy into English generally suck. If you want to learn still more languages, it would do you no harm and a world of good. Italian, Spanish, Russian, Arabic and Hebrew are all of great relevance to the study of Western philosophy, and heylookit that we haven't begun to address Eastern philosophy yet. Not that there is one homogenous Eastern philosophy corresponding to Western philosophy. Mandarin is relevant to Confucianism and Tao, and Sanskrit and Japanese to Hindu-Buddhism.
I don't really know squat about Eastern philosophy. Back in the West, once you've mastered Greek, Latin, German, French, Italian, Spanish, Russian, Arabic and Hebrew, you may begin to keenly feel the lack of Portugese, Catalan, Provencal, Danish, Polish, Coptic and/or Armenian, to name just a very few. And the fact that I've so far mentioned Arabic, Hebrew, Coptic and Armenian only as they related to Western philosophy may have already led you to suspect it, but let me come right out and say it: I know significantly less than squat about Muslim/Arab/Middle Eastern philosophy. Although I may have a vastly greater idea of how much I don't know about it, how much is there unknown by me, than does the average Westerner.
But screw average! Philosophy doesn't have much to do with being average. Not Western philosophy, anyway. So screw the average person giving you advice about studying philosophy and telling you to start with Plato. That advice has cost the world an immeasurable amount of wisdom, because most of us hate Plato. (By "us" I mean "people," whether philosophers or not.) Start with almost anybody except Plato: the Pre-Socratics, or Aristotle, or Zeno, or Diogenes, or Epicurus. Or Machiavelli (Yeah! He'd be a GOOD one to start with!), or Hume, or Nietzsche. Just not Plato. Or Plotinus. Or Hegel.
If you're even the least bit inclined to start with Aquinas, or Augustine, or Barth, leave me alone and go and ask a theologian for advice, and if you want to call what you're studying philosophy, or even the greatest of Western philosophy, that's your own business, and many other theologians will agree with you. Mazel tov.
Okay. Now that we've gotten rid of THOSE jerks -- you're going to have to read Plato at some point if you're to become a great Western philosopher. There's no getting around it because all of the other great Western philosophers from his time to ours also had to deal with him, and if you don't read him you often won't know what they're talking about. Now, if you're unable to summon any enthusiasm for Epicurus or Machiavelli or Nietzsche, you should probably just face the fact that you're not going to become a philosopher. But don't be mad at me, because I saved you from having to study Plato -- and, you're fluent in 15 or more languages, and believe me, that's going to come in handy no matter where life takes you.
And I haven't said a word yet about the cultures of the indigenous peoples of the Western Hemisphere! Ah, many more languages here to be studied. Probably most of my readers are from the United States, and may not realize the extent to which the languages of the Aztecs and the Incas and the Mayans continue to flourish in Latin America, with several million native speakers each. The most widespread indigenous language in the US, Navajo, is spoken by fewer than 200,000 people. So you can study the more widespread languages because they're more widespread, or the less widespread languages because they need more support -- or both? Who's stopping you?
Not me! But what I actually know about has more to do with the European and Middle Eastern languages, and besides the ones I've mentioned above, you could learn Icelandic and Norwegian and Swedish, and Basque, and Finnish and Estonian and Hungarian, and Czech and Slovak and Slovenian and Serbian and Croatian and Bulgarian, and Gaelic and Welsh and Breton, and Albanian, and Lithuanian and Latvian, and Turkish, and Ukrainian and Belorussian and Macedonian, and Rumanian and Moldavian, and Kurdish, and Maltese. And Georgian! And I've left out a lot, not intentionally, but because the region between Greenland and the Caucasus is an incredibly rich linguistic quilt. And because translations really do suck, or at least especially most translations of philosophy into English. Being multilingual really will open up new worlds for you in a way which monolingual people simply can't imagine. Which means that monolingual native speakers of English are ironically at a disadvantage because of the power of our language, the same way that monolingual native speakers of French were at a disadvantage as late as a century ago when French held an international dominance similar to that held by English today, the same way that monolingual native speakers of Greek were at a disadvantage 2000 years ago in the Graeco-Roman world because everyone adored Greek culture and Greek was the dominant international language and the monolingual Greek-speakers despised Latin without even knowing anything about it, much as many Americans despise Spanish without having a clue about what they're missing, even with the Nobel Prize committee trying mightily to give them a clue by giving Lit prize after Lit prize to authors in Iberia and to the south of us.
Most (not all!) of the ancient Greek philosophers had little knowledge of languages other than Greek. This show us that progress has occurred in philosophy as in other things. Some people might tell you that I'm yankin' ya here, that the title of this post has promised you something I have failed to deliver. But those people are wrong. And the best advice they'll give you is something like urging you to read Will Durant. And that's not very good at all. If you want to have a chance at learning philosophy deeply, and even a chance at becoming a significant philosopher yourself, I'm the kind of guy you need to listen to. Listen up very carefully, kids, here comes the punchline, and it's a good one:
Look at ALL of the great modern Western philosophers: Machiavelli, Descartes, Bacon, Hobbes, Spinoza, Leibniz, Voltaire, Hume, Kant, Goethe, Schopenhauer, Marx, Kierkegaard, Nietzsche, Shaw, Heidegger, Santayana, Russell, Sartre -- there is very, very little that all of them agree about. About the main tenets of their various philosophies they are often in the bitterest disagreement: you've got devout Christians alongside atheists, some far Left politically, some far Right, and some with a hearty contempt for both Left and Right. What do they all have in common?
They were all multilingual, that's what. Boom.