When it comes to the word 'core' the uninitiated automatically think of 6-pack abs, situps, leg raises, and planks. But wait! There's MORE!
Think about your core like a box.
You have the abdominals and hip flexors in the front, obliques on the side, erector spinae & gluteals in the back, even including the pelvic floor muscles, multifidi, and the hip musculature. It's important that ALL of these muscle group participate in the majority of the movements you do daily whether it be squatting down to pick something up or reaching to get something from a shelf.
So crunches and russian twists aren't the only thing I can do for my core, got it. What else?
Core training requires many types of movement patterns, and it's hard to train all of them in one workout session so it would be best to spread it out over 2-3. Also, it is important to take programming slow, as many beginners have weak, untrained core muscles. For preventing lower back pain, it is important to center your core training program around endurance. Here is a list on how to train the core for all sides.
Supermans, half supermans, and back extensions will train the glutes and erectors dynamically, extending the spine. Squats, deadlifts, and goodmornings are also awesome in training the back (as long as the spine is kept neutral!)
Side bends, cable chops, landmines, and russian twists are the go-to for training the oblique muscles dynamically to laterally rotate and laterally flex the spine. For isometric work, do side planks and HEAVY farmer's walks. You could also do unilateral exercises using only one arm for any exercise (single arm bench press, single arm curl, etc.)
Leg Raises, crunches, and reverse crunches will train the core dynamically, flexing the spine. To train the hip flexors, flex the hip! Knee raises without tilting the pelvis posteriorly will train these, but often they're very tight in individuals so I personally don't include them much when desigining programs. To train it with anti-extension, in other words isometric, you could do planks and ab wheel rollouts.
Those are just a few exercises for each side of the core. A very general, non-individualized way to program this would be performing 3 exercises from the front and 2 exercises from the side on your first workout day, and then 3-5 exercises from the back on your second workout day; 2-3 sets of 10-15 repetitions (depends on your skill level)
Enjoy! Please visit my profile and email me if you have questions.