Generally for a 4-connected grid graph the Manhattan option should be used as it is the true distance on a 4-connected grid. For an 8-connected grid graph the Diagonal Manhattan option is the mathematically most correct option, however the Euclidean option is often preferred, especially if you are simplifying the path afterwards using modifiers.
For any graph that is not grid based the Euclidean option is the best one to use.
Manhattan => 4-connected grid graph
Diagonal Manhattan => 8-connected grid graph
Euclidean => not grid-based graph
For the hexagonal grid graph, which is the 6-connected grid graph, which Heuristic should I use for it?