We have two locks we use.  A simple sliding patio bolt (like a ranchslider bolt).  You can lock when required from both inside and out and its very useful with a busy family coming and going and not wanting to lock each time.
Our deadbolt is the most popular option.  A key is required to shut the deadbolt.  However we now have a magnet solution which allows the door to clunk shut without having to key each time.