Waxing is a process of applying a soft waxy layer over your skin and the hair above it. This could be a wax strip or melted wax beans. It is applied in the direction of the hair growth, which is then pulled off, leaving the hair from its root. This is a painful process because the wax often sticks to your skin and pulling it apart would indeed cause you pain.
Epilating is a process done using an electrical device that pulls off the hair from the root and does not cause much pain to your skin. But mild irritation persists, which will go if you get used to the epilation process and your skin gets used to the sensation.
Shaving is a process in which you have a razor or a shaver that is rolled over the hairy part. It removes the hair only from the surface of the skin and not the root. It is not at all a painful process. But you need to keep on doing it every 2-3 days because hair does not come off the root and keeps growing afterward.
Out of these three methods, if you need to have a long term result, it is better to invest in an epilator. Though it is a little painful, you will get used to it after using it for 2-3 times. So, choose an epilator device over shaving or waxing.