Oh, this sounds fun! For me, the first words I usually pick up on are the way they address others: -san, -kun, -chan, etc. Then after that I usually learn their word/words for I like/love you: daisuki, sukidayo, aishiteru.
But now that I think about it, I learned from watching anime. I still think I picked up on how they called each other first, but I think chibi may have been one of my first words I learned from watching Fullmetal Alchemist. XD