However if you are doing this for real use, or if it's for an assignment that doesn't say anything about what kind of list
you should use, then you should definitely not spend any time writing low-level code to work with lists. Instead, choose a standard List from the standard Java API -- it doesn't really matter which one you choose since your data is small, so ArrayList is as good as any other choice.
Then you can have a class that adds and deletes customers that's very simple, basically one line of code per method. To sort a list, there are also standard methods like Collections.sort(list).
Here is a tutorial about lists and other collections.