in push over analysis, the structure should be loaded to full collapse (unstable condition), if you use displacement controlled push over, you should be sure that target displacement is large enough to cause full collapse.
The allowable drift in most codes is about (H/400 to H/600) and reduction factor is ranged between (3 - 8 ). hence the max. inelastic drift is about ( H/200 to H/50).
Consider material factor of 1.5, So I suggest target displacement of (H/20 to H/30)
Pushdown analysis method consists of analyzing the structure, which has suffered loss of one or more critical members, under increasing gravity loads. The gravity loads are incremented until collapse of the structure occurs, defined as an inability to support the applied loading.
As for Pushover analysis, it is for checking how much load (when using force controlled push over) or displacement (when using displacement controlled pushover) in either X or Y direction can a building take under monotonically increasing load or displacement. In a way giving you its seismic resistance properties.