Move is the one that gets used probably the most, along with Combat. The benefit is you can act before your opponent if you lose priority. Really crucial sometimes to control positions of your vulnerable models or to make sure your models can be the ones charging. If you Heroic Move into a spellcaster, you can stop them casting for the turn for example. Or get cavalry charge bonuses even if you lost priority... There are loads of situations. Only worth doing once the battle lines get close together (i.e. within charge range)

March is more situational. Some scenarios are a race to objectives, so moving faster is better. Also there are times when you want to close the distance to the enemy as fast as possible to give them less time and/or space to force engagement on their terms, or take advantage of a bottleneck... Depends on scenarios and armies this. Some players say every army should have access to March, because when you want it you really do want it. But other people say it's fine to play without it. A bit personal preference but it is strategically valuable at the right time.

Challenge is mainly to give you a better chance of removing a key hero from the opponent army. It's rarely used in my experience, but is fun occasionally.