Your Eiffel Tower tickets will buy you however long you'd like to stay inside, but most people spend between two to three hours inside. Remember, the climb up can be quite intense and you might want to stop to catch your breath at several points. You can pretend to be admiring the views while you do this.
It usually takes about 30-45 minutes to climb the stairs up to the second floor. Plan to spend at least 1.5 hours on the first and second floors, or 2.5 hours if you also plan to visit the top.