The plank is the one bodyweight "core" movement that's actually worth your time.
Your body is a plank, as the name suggests. You are a single cohesive unbroken body, a straight line from head to foot. Elbows/forearms and toes are your only points of contact with the ground.
Simplified Progression
1. Forearm/knee planks (male and female, two minutes)
2. Hand/feet planks (male and female, two minutes)
Movement Mastery:
male and female, two minutes