First, a bit of history about the tale. Beauty and the Beast was originally (as far as we know) published as a novel in 1740. A few years later, 1756, Beaumont wrote a condensed version. This is the one we read.

Beauty is not an only child, so there is nothing in that context unique about her -- she is one of six children.

However, Beauty has a unique outlook on life -- she (eventually) sees the inner beauty of Beast -- particularly when she returns to the Beast's castle and finds him nearly dead. She suddenly realizes that she does indeed love Beast.

And that love breaks the curse -- much like love's first kiss from other folk tales.

I don't think it is an accident that the father encounters Beast's castle. From the stand point of the story, he had to encounter Beast. It is also no accident that Beauty's sisters deceive her about staying at home longer than Beauty promised -- that adds to the tension of the narrative. Beauty must pass the test.

Beauty and the Beast is, among other things, an internal journey of self-discovery for both Beauty and the reader.

And one last thing -- Beast seeks Beauty. Indeed, Beast knows he will marry Beauty.