Which Tone of Speech Should I Learn First?

Question today comes from Junil Jung in Chicago, Illinois in U.S.A.

I am studying to go to Yonsei Korean Language Program in summer. I took a look at their textbooks, and they were teaching -니다 form. I read your note and understand the difference between -니다 and 아/어요 form. My question is, which one should I have learned first? 

Tone of Speech 101

Question today comes from Johanne from Austria:

My teacher taught me -요 form. But when I talk to Korean people, they keep on correcting me and ask me to use -다/까 form. I am confused. What's the difference?