They're = they are
ex: They are nice people/ They're nice people (they= pronoun + are= verb)
There ex1: There are a lot of apples in the basket. (don't know what type of word it is,though)
ex2: I don't want to go there! (I don't want to go to that place, adverb of place)
their= possessive pronoun, the correct one here
ex: I love their house. (the house that belongs to them)