First - people still talk about "core" in the wrong way. Situps are not core exercises, they're a hip flexor
exercise, and not a great one at that. Crunches are "ok", but really there's an entirely better way of looking at how to work your core:
Think of your core as doing four things:
1.) Bracing your spine so it doesn't snap forward
2.) Bracing your spine so it doesn't snap back
3.) Bracing your spine so it doesn't snap sideways
4.) Bracing your spine so it doesn't rotate
So the smartest play is to make it do those things! Planks and bridges are your best friends in the world of core work.
Or another way to think about it would be to "plank in all four directions".
Then we add in the single leg stuff so we get the rotational bracing. Simple. Easy. AWESOME core workout.
BEST CORE WORKOUT EVER:
1.) Single Leg Plank x 0:30 L+ 0:30 R
2.) Side Plank x 0:30 L + 0:30 R
3.) Single Leg Hip Bridge x 0:30 L+0:30 R
Repeat that circuit until you feel like you "got what you came for" =)
AWESOME BEGINNER CORE WORKOUT:
1.) Plank x 0:30
2.) Opposite Arm Leg Raise x 1:00 L + 1:00 R
3.) Hip Bridge x 1:00
You still get the rotational core work with the Opposite Arm Leg Raise, and you still get the flexion/and extension core work with the plank and the hip bridge. This is an AWESOME place to start.
And since people still ask - here are the muscles getting worked:
Anti-Flexion: Glutes and Spinal Erectors
Anti-Rotation: External Obliques and Internal Obliques
Anti-Lateral-Flexion: External Obliques, Internal Obliques and Glute Medius
All of these pictures are from my first book - The Stubborn 7 Pounds: How to Go from Good to Rockstar. It's probably the most "complete" book that I've written. While the followup books are very focused, it covers everything.
In System Six: Easy Fat Loss, I deliberately "left room" for other stuff. Essentially what ever you like - running, yoga, martial arts, physical therapy, corrective exercise, or even just prepping your food. If you don't have anything else to fill in the extra with, I'd add in this core circuit.
ABS ARE STILL MADE IN THE KITCHEN
You want to have solid core strength mostly because it protects your back and allows you to go stronger in more advanced full-body-fat-loss exercises like kettlebell swings, squats, deadlifts, single leg deadlifts, military presses, ect.
So while *building* your core strength happens in the gym, being able to *see* a lean hot sexy core comes from what you eat. The maxim still stands - if you've got a layer of fat over your abs, doing a core workout isn't going to change that.
So lose the fat on top of your lean hot athletic body by what you eat, and build the lean hot athletic body inside through your workouts.