What should someone prioritize when deciding to add automated tests for an application that has already been in the market for a long time(3-4 years) though it still receives updates? Assume that most of the obvious bugs have already been found and the GUI shouldn't change other than new additions.
E.g., assume that this application is Calculator with a login functionality that if used, allows you access to scientific and financial views. Normally, among others, I would test that drop down menus have all the options available, buttons are of same size and at the correct place, login functionality, the scientific/financial views are available only after login and of course the core functionality which is what happens when each button is pressed. New updates could include a new view(e.g. programming) or additional buttons in existing views.
Which of those tests should I still automate?
Relevant book, article proposals, your experience are all welcome.
Edit: added the calculator example.