Thinking about balancing the shoulder in terms of the big movements is difficult and self-defeating. The shoulder girdle has numerous individual movements that occur simulatenously in different patterns and to greater or lesser extents to effect the movements we understand - push; pull etc. To illustrate this, take Bench Press and Bent-over Rows. On the face of it, these would appear to be the polar opposite of one another. Bench involves flexion at the glenohumeral joint, whilst rowing involves extension. However, good technique in both bench and row requires scapular retraction and, to some extent, depression. A more physiological comparison would be the pressup and the row, in both of which the scapula is not anchored and can move more freely.
Bench pressing and Overhead Pressing promote balance in terms of scapular retraction and depression vs. protraction and elevation, but both involve glenohumeral flexion (the role of the anterior deltoids). Too much strength in this movement can lead to impingement issues in the shoulder.
The fact is that the big movements all have some overlap in terms of the different articulations at the shoulder girdle. Keeping the shoulders healthy, which should be your aim, involves identifying any ROM discrepancies; establishing proper movement of the scapulae in all directions and correcting specific weaknesses when you find them.
Typical ROM problems are: decreased internal rotation, decreased flexion (putting the arms overhead), reduced thoracic spine extension.
Proper movement of the scapulae involes activation of the serratus anterior, lower traps primarily, but gaining proper proprioception in all movements is worthwhile.
Specific weaknesses tend to be external rotation of the glenohumeral joint, depression, retraction and upward rotation of the scapula and extension of the thoracic spine.
This is a pretty limited overview of shoulder health but if you search for the things I mentioned you should understand better how to balance things out and keep your shoulders healthy.