I'm in my late 20s and a nest egg is years away, but having a a basic emergency fund and financial safety net did wonders for my peace of mind. For those who haven't done it yet, I think it's the most important financial goal to hit as early in your career as you can.
Long-term disability insurance and life insurance are nice to have too. Patio11 has been preaching this [1] but it took me a while to really get it. The technical detail of "own occupation" is really important here.