Which sentence fits best?

Let's put the case that I travel to a foreign english-speaking country and the man at the airport desk asks me about the purpose of my travel. What would be the correct answer to make him let me pass?

"Why did you come here?" - "I will be staying here to learn english at place X"

- "I came here to learn english"

- "I came here for studying english"

- "I will stay here to learn english"

I would tend to the first example sentence...but I don't know why.

Thank you!