Join this 60 minute ladder flow for the core. As Swami Kriyananda often said, "that's where the real spiritual work takes place."
As for the physical core, remember that core means your back muscles as well as your abs. The stronger it is, the less effort simple movements take, and the more energy you have for your yoga practice. So get your core stronger and join me on the mat. Level 1-2, no props needed.