Setting aside proclivities to particular fields, eg. interested in computers, so study computer science.
I'm wondering which degrees develop well-balanced, clear thinking, and satisfied students?
Which degrees equip one to live a good life? Or is this an unrealistic expectation from institutions of education?
Physics IMHO. It's weight lifting for the mind, teaches you judgement, precision, and abstraction while insisting results be grounded in physical reality. What better skills for the acquisition of wisdom?
Get in some classical philosophy if you can, as Aristotle answered the question beneath your question - how does one become wise? One becomes wise by imitating the actions of a wise person.
Physics and Aristotle provide the escape from modern philosophy which emasculated itself with the phrase "normative statements cannot be derived from empirical observations". More commonly stated as "you cannot derive an ought from an is".
For me it all led to a study and practice of the oldest Buddhist material in the Pali Canon. This is quite different from the semi-digested pap offered up as "mindfulness" these days. Fascinating stuff, sharing the qualities listed above for Physics.
Best of luck and don't forget to enjoy it all.