What books might you recommend on finding out more about Mary?

If you’re looking for a general overview, I recommend The Catholic Companion to Mary, by Mary Kathleen Glavich.  This highly readable book covers key events of Mary’s life and explains Catholic teachings/beliefs about Mary.  It also has all kinds of Marian trivia (everything from her influence on female names to the definition of a “Hail Mary” pass in football).
It’s out of print, but the book  Mary in the Church: A Selection of Teaching Documents can be purchased used on Amazon.  It contains four recent Church documents on Mary, including the National Conference of Catholic Bishops’ 1973 letter Behold Your Mother: Woman of Faith, which is one of my all-time favorite resources about Mary.  
If you are interested in Mary’s role in sacred Scripture, the Scott Hahn book Hail, Holy Queen is a terrific resource. It covers the Biblical evidence for the Catholic Church’s teachings about Mary and points out some connections that often surprise Catholics and non-Catholics alike.
On a totally separate note, I have a personal fondness for Beverly Donofrio’s memoir Looking for Mary: Or, The Blessed Mother and Me.  It’s a frank, appealing story of a lapsed Catholic who, rather unexpectedly, develops a strong connection to Mary.
And if you’re interested in modern women’s perspectives on Mary, you can check out my own book Mary and Me: Catholic Women Reflect on the Mother of God, which shares the personal stories of women from their twenties to their nineties.
Happy reading!