I am thinking of reading a book by  Philip Larkin, any recommendation?
He's got quite a few good works. I would recommend A Girl in Winter, or High Windows.
Could you tell me what is the story about in A Girl in Winter?
It's a book about a librarian who leaves work to help a colleague who is sick. High Windows on the other hand, is a collection of poetry. 
I am not a fan of poetry so I think I will go with  A Girl in Winter, sounds intriguing, is it a fantasy novel?
Sort of. It's a bit more of a love story, but it's been a while since I have read it. It was published in 1947.