There are hundreds of push-up and plank variations. The key to doing good push-ups is to ensure you start and maintain a good stable core and spine throughout. You shouldn't pike or allow your spine to sag while doing push-ups or planks. Once you get into an up push-up position find a good spine position by tilting your pelvis, fulling flexing, and extending your back a few times. Once you are aware of those two end positions, position your back and pelvis halfway between those two end ranges. That is a good start position, then screw your hands into the ground to set your upper body. Finally, using a band to assist you can also be a good way to start since it will help enforce good positioning and decrease the amount of load place on the upper body.