Phrases like "Sorry, I don't understand!" and "What does X mean?" and "How do you say X in Y language?" and "Do you speak English?" and "I don't know / can't speak much of X language!" are among the most value phrases I like to learn ASAP when trying to speak a new language...
How about you? What phrases have been your favourites? Which ones would you start with if learning a new language? Which phrases have got you out of problems many times?
I can only talk about classes as I've never needed it in actual practice but besides the two you mentioned about "what does X mean" and "how do you say X in Y language" I always learn "can you please write that in Skype" and "can you repeat that please" when having a lesson. This is because sometimes I have trouble catching something said so first I ask if they can repeat it and if I still don't understand, I get them to write it. This also gives me the opportunity to make flashcards after the class with any word I didn't know.
I think in an actual conversation, can you repeat that? and can you speak more slowly? would come in handy.
Next I would like to learn "please" or how to make a request politely, and basic phrases like "How do you say [word/phrase] in Persian?", "May I have [thing]?" and "What is [thing]?"
This is an interesting case because I'm dabbling in this language out of cultural interest, and I have no expectation of traveling to a Persian-speaking country any time soon.