It actually depends on the level of the students, like undergraduate or postgraduate; however, for me the best books are Kuby Immunology and Janeway's Immunobiology, mostly used at higher levels. If you like too classical immunology book for undergraduate level Roitt's Essential Immunology is also fine.
One of the best book I have gone through is Prescott Microbiology by Willey. In this book the chapter Immunology has described elaborately with so many color images. Please go through at least once..
We can say basic books in stead of classic as you said , for me , i advice you to read KUBY Immunology or Immunology from Eric Espinosa (Author), Pascal Chillet (Author) . These two books can give you a general overview about Immunology science , clarify the big titles and explain you basic concepts and even deep notions with extremely details .
The answer to this depends upon whether you want to learn mouse immunology or human immunology or 'classical' immunology. These are not equivalent!
My recommendation is also influenced by how much background knowledge you have. Previously mentioned textbooks are all very good, all out of date, and not all that easy to read (especially if your native tongue is a language other than English.)
For entry level I recommend Abbas & Lichtman's 'Basic Immunology - Functions and Disorders of the Immune System' or Playfairs 'Immunology at a Glance'.
For advanced level I recommend 'Janeway's Immunobiology', Parham's 'The Immune System', Sompayrac's 'How the Immune System Works', Abbas' 'Cell and Molecular Immunology' and Roitt's Essential Immunology'.
Immunology is conceptually challenging. After teaching it for 20 years, I have learned that that the accuracy and quality of diagrams are the most useful measure of a good textbook!