If I am be adding an unknown number of elements to a List, and that list is only going to be iterated through, would a LinkedList be better than an ArrayList in the particular instance (Using Java, if that has any relevance)
The performance trade-offs between ArrayList and LinkedList have been discussed before, but in short: ArrayList tends to be faster for most real-life usage scenarios. ArrayList will cause less memory fragmentation and will play nicer with the Garbage Collector, it will use up less memory and allow for faster iteration, and it will be faster for insertions that occur at the end of the list.
So, as long as the insertions in the list always occur at the last position, there's no reason to pick LinkedList - ArrayList is the clear winner.