In the book The Lovely Bones by Alice Sebold, what are readers' expectations about the story?How can I express a personal connection to this book...

You have asked an interesting two-part question here!  First of all, a reader experienced with Alice Sebold's writings probably has very high expectations in regards to the story of The Lovely Bones.  You see, Sebold's first book was actually a memoir of her own rape.  The book was called Lucky because Sebold herself was told (according to Wikipedia) that she was "lucky" not to have been killed because another young woman of a similar age (18) was both killed and dismembered in the same tunnel where Sebold was raped.  Through this memoir, Sebold herself says that she wished to bring "more awareness to rape."  She certainly did. 

Anyone who read Sebold's memoir would wonder whether Sebold would continue to explore this subject in the context of fiction.  She does.  Upon first glance, a title like The Lovely Bones immediately brings a murder to mind.  One wonders whether Sebold was considering the "unlucky" woman from her previous memoir while devolping the character of Susie Salmon.  Considering Sebold's memoir won awards, the expectations were high for her second work. 

Sebold did not disappoint.

The second part of your question implies that many readers, perhaps, did NOT know of the high expectations involved (perhaps not even knowing about Sebold's first memoir).  In that case, the expectation would most likely be that this is a story about a beautiful young girl who is both murdered and somehow reduced to bones.  This is true, although ironically not what the title fully means.  Why a young "girl" instead of "man"?  Because young men are usually not referred to as "lovely."  Why "murder" instead of, let's say, a medical school skeleton specimen?   Hmmmm, just a guess.

Further exploring the second part of your question, you should ask yourself a few questions:  Have you ever been afraid of being raped?  Have you ever been afraid of being murdered?  Have you ever been afraid of losing your life too soon?  Have you ever known someone, a certified "loner," who kept apart from society and aroused suspicion?  Have you ever experienced the variety of ways people can deal with the loss of a loved one (different ways of expressing grief)?  My answers to those questions are going to differ from yours.  For me, my personal connection to the novel is the absolute horror and fear of the same thing happening to one of my daughters.  This connection makes Susie Salmon's murder scene absolutely unbearable to me.  Your answer will depend on your response to the above questions.