Collections are used to express several orthogonal concepts in programs. In principle, you should express yourself as precisely as possible. With collections, this means using the most general possible interface as a declaration and the most specific implementation class. However, this is not an absolute rule. I carefully went through JUnit and generalized all the variable declarations. The result was a mess, because there was no uniformity. The confusion of having the same object declared as an Iterable in one spot, a Collection in another, and a List elsewhere made reading the code more difficult without much payoff. It was clearer to just declare every variable as a List.
The first concept expressed by collections is their size. Arrays (which are primitive collections) have a fixed size, set when the array is created. Most collections can change size after they are created.
A second concept expressed through collections is whether or not the order of elements is important. Calculations in which the elements affect each other or where external users of the calculation attach importance to order call for collections that preserve order. The order may be the order in which elements were added or it may be provided by some outside influence like lexicographic comparison.
Another issue to be expressed by collections is the uniqueness of elements. There are computations where the presence or absence of an element is sufficient, others where an element needs to be able to be present multiple times in a collection for the computation to be correct.
How are the elements accessed? Sometimes it is enough to iterate over the elements, doing some calculation with them one at a time. At other times it is important to be able to store and retrieve elements with a key.
Finally, performance considerations are communicated through choice of collection. If a linear search is fast enough, a generic Collection is good enough. If the collection grows too large it will be important to be able to test for or access elements by a key, suggesting a Set or Map. Time and space can both be optimized through the judicious selection of collections.