The plank is a very good exercise for your core muscles. Many people think that they should hold the position as long as they can, but that is not the optimal way to do it. You should do it in 15 seconds intervals. Be in the plank for 15 seconds, pause in 10 seconds, then the plank for another 15 s and so on. This is the best way, because you have a better ability to do this exercise right, when you only stand in 15 seconds. If you stand as long as you can with no breaks, you will begin to lower your stomach, your shoulders will get into a crooked position.
The side plank is harder to do. Not as much for your center core as the “real” plank, but this one trains the oblique abdominals and especially your shoulders and the outside of your legs and buttock. There is a huge load on the supporting shoulder and leg. It is also hard to lift the top leg. If you want an lighter version, just have your legs together. Be aware that your hips are not hanging. You body has to be in a straight line. This exercise you shall not do for more than 10 seconds per interval.
Love, sweat and wisdom