1) A popular language (like Spanish or Japanese) can boost your job opportunities.
2) A popular language lets you talk with more people.
3) A somewhat less widespread but strategically important language (like Turkish or Arabic) can help if you're in politics or the military.
4) Learning the language of your ancestors is good for genealogy and personal satisfaction.
5) Learning a rare language (like Lakota) can help preserve it from dying out.
6) Learning a regional language (like Welsh or Manx) is a great way to express and maintain identity.
7) Learning any language with phonemes not used in English, if you can pronounce them, gives you a way to shush babbling-age babies. Unless extremely distressed, they tend to be fascinated by new phonemes and will fall silent to listen.
8) Learning any language at all, including constructed ones like Klingon, is good for your brain and your intellect; and every language you learn makes subsequent ones easier.
And to answer the essay's title question, beyond goal-related stuff covered above:
1) If you are not good at languages and want to make it easier on yourself, pick a language with some kind of close connection to English: German (because English is a Germanic language) and Spanish or French (connected through Latin, and both fairly regular) are good choices.
2) If you are good at languages and want to maximize the usefulness, pick something without a close connection: Russian (gives you access to central & eastern Europe) or Japanese (a popular Asian language with ideographic writing) are good choices.
3) If you want to maximize your opportunities to use the language, pick one of the globals: French, German, Japanese, or Spanish. These are languages active in multiple countries and popular among diplomats, travelers, scientists, and businessmen. Arabic, Chinese, and Russian are also well worth considering.
4) If you want to do the most good, pick the rarest language you can access -- but it's up to you whether you want one with a strong core trying to save it, or one without. Welsh, Hawaiian, and Cherokee are small compared to major languages but they have a thriving culture and a goodly batch of literature to enjoy. Tiny languages are dying out rapidly and need all the help they can get; many are spoken by indigenous people whose cultures are being stamped out. Helping save an endangered language is like helping save an endangered species.
In case you're curious, I've had a little formal study in Spanish, Russian, and Japanese. I've paid enough attention to Welsh, Cherokee, Lakota, Arabic, Turkish, LAadan, and Sindarin that I can recognize some words. It's even gotten to where I'm processing heiroglyphs as "language" rather than "art" and trying to pick out the handful of symbols I recognize. (You'd be amazed how often they are done wrong.) Plus, of course, a smattering of pretty much every language I ever brushed up against. And the ones I've invented myself (or more precisely, collected from other worlds).