Or should I still do shoulder presses or other shoulder exercises or is doing military press sufficient?
military press targets the front delts
link shows the synergist muscles that help, but its primarily a shoulder exercise...but a hard one that pulls in lots of other muscles to help and to stabilize...hence its superiority to, say, front raises.
It will help the shoulders, but you need to change the exercise up every 1-2 months because the CNS and musculature adapts to the exercise and stops growning.