Correct. Each wound is placed one at a time, in the order that the FP chooses.
The "stack" is a concept from Magic, but it also is used in LOTR and Star Wars. Essentially, there is only ever one action going on at any given time. Other actions may interrupt or affect that first action, and so they get placed on the "stack." Only the top action in the "stack" is occurring. Anything below that is suspended until the topmost action is completed and then removed from the "stack."
Here is an easy example of suspending an action while a new subset of actions is occurring:
Frodo is facing a damage +1 minion. Upon losing the skirmish, he is required to take 2 wounds. The first wound is now on the stack. As a response to this first wound, Frodo puts on the Ring and takes it as a burden. The Shadow player then responds with
The Ring Is Mine! to add an additional burden (note that the second wound from the damage +1 minion is still at the bottom of the stack; it hasn't happened yet).
Tolman Cotton then responds to TRIM to prevent the burden.
Once Tolman does his action, all of the sub-actions have come off the stack, and the second wound from the minion may now be placed.
So yes, Sam taking the Ring
can interrupt actions such as the Berserker.