When someone is using Ghaston (or any other effect), at what point does the cancel happen? Is it after the cost is paid? Is it after targets are chosen? Exactly which parts of the text are considered to be 'initiation'? I ask because obviously the decision to cancel or not is very dependent on who the target ends up being. Clearly this is a Do X to Do Y situation. In general are both X and Y the initiation?

Ghaston Text:

Challenges: Return a Martell character you own and control to your hand to choose an opponent's character. Return that character to its owner's hand

The cost is paid and targets are chosen. So you would say "I'm going to return my myrcella (she is now moribund: hand) to bounce your Stannis (he is not moribund yet because the effect hasn't resolved)." Then your opponent can use his cancel so Stannis never becomes moribund and Myrcella still returns to hand since she was already moribund.

The cost and applicable targets are chosen during the initiation. The cost paid is immediately put into the moribund state if it involves cards being removed from play to pay the it. Targets or selected cards to be affected by the effect are only put into Moribund during the Resolution step if the effect had not been canceled.

The only time that I recall a target as not selected or chosen during initiation is during Then segments of an effect. "Then" segments of effects "initiate and resolve" during the step 3 of effect resolution.

a) Determine the cost (to either marshal the
card or pay for the card's effect) or costs (if
multiple costs are necessary for the intended
action).
b) Check play restrictions, including
verification of applicable targets.
c) Apply any penalties to the cost(s). (Any
effects that modify a penalty are applied to that
penalty before it becomes a part of the cost.)
d) Apply any other active modifiers (including
reducers) to the cost(s).
e) Pay the cost(s).
f) Marshal the card, or trigger the effect.
Choose targets (if applicable) and proceed to
the save/cancel step.

Those are all the things that happen during initiation of an effect and/or action.