First useful words to learn in a foreign language…
… depends on how old you are!
A toddler can’t tell the difference between language A and language B consciously, so there’s no point for him to learn “How do you say ‘XXX’ in English”. Instead there’s always the danger of the toddler doing things to accidentally hurt himself or herself, so it’s more useful to teach the toddler the foreign equivalents of simple words like “Daddy” and “Mummy” and “help” so that he or she can sound out when hurt or in danger.
Meanwhile, an adult who learns “Hola” in Spanish can only say hi to a new Spanish-speaking friend using that and then feel awkward for the lack of words to continue the conversation. Instead, it might be better to learn the foreign language equivalent of these questions e.g. “How do you pronounce / say / write this in language X” and “I didn’t understand. Could you repeat?” and “I’ve got a question. What does this word mean?” These are questions that can help you to pick up the language more quickly.
Finally, a professor or high ranking official needs to maintain his position of authority and cannot be seen to ‘not know’ anything, so if they speak in a foreign language, they need to already be extremely fluent in it. So the first useful words for them is probably an entire speech about thermodynamics or the country’s economy.
For me, I also recommend learning how to ask questions to which you already know the answers in terms of content. For instance, now that I am in Singapore, “What is your impression about Singapore?”. (e.g. In German: “Was ist dein Eindruck von Singapur”, In Mandarin: 你对新加坡的映像怎样？) is a very important question to ask my foreign friends whom I meet here :D You will probably already expect some of their answers. While you leave it open to them to answer it in their language, you can probably pick up new expressions as they describe what they think to you. And you can be sure that most of the time, it’s not just a yes or no answer if you’re sincere about it😀
So what are some of the first words you would learn in a foreign language?