How do movement priorities work in detail, for both players and AI?

For player-controlled minion movement: First, count the hexes in valid terrain, usually path unless your minion can move on other terrain, between its starting hex and its mark, using the shortest route possible. Count through units, but not landmarks or spires. Second, find all the hexes it could end its movement on using its full movement, considering that it cannot move through units unless specified, and count from those hexes to its mark. If any are closer to its mark than its starting hex, that is where it moves. If more than one is closer to its mark than its starting hex, it is your choice which of those hexes the unit moves to. Third, if it cannot get closer using its full movement, subtract 1 from your movement and find the hexes it can now end its movement on. See if any of them are closer than its starting hex. If so, those are now its ending hex options. Fourth, repeat the third step as needed. Fifth, if there are no hexes at all that it can move to that will get it closer to its mark, that is when you can start looking at hexes that get it no closer and no further away, using any amount of movement. This is considered a lateral move. It can move to one of those hexes, or it can stay where it is. Also, a tip for counting to your minions' mark: if the path bottlenecks down to a single path on the way to its mark, you can just count to the entrance of that bottleneck, because it is always going to be the same number of hexes between the start of the bottleneck and its mark. AI-controlled unit movement follows the same five steps, with one difference. Where a player would get a choice between multiple equally valid ending hexes, the AI unit instead moves to the hex that is closest to its mark. On a lateral move, it can move to one of those hexes or stay where it is, at the player's choice.