A plank on your hands with straight arms — the position half the moves in the gym start from, and a solid core hold on its own.
Every move in Core Buddy has a video like this one — and it builds the whole session for you, timer and all. Free to download.
The high plank from your knees. Same position through the shoulders, easier to hold. Work with this version for as long as you like — when the full one feels within reach, give it a go.