Which branch is best to join as an officer having no military experience and 2 degrees?

The question really comes down to your personal interests. The Air Force and Navy lean more toward the technical areas. From what I've seen and officers I've known, the Air Force is rather stratified by being a pilot or not. The Navy is rather old school and the Officers and Enlisted personnel have strict lines of separation. It's just the way it is. The Coast Guard pretty much follows the Navy model.
The Army and Marines are more blurred in terms of Officer/Enlisted mingling (eating, living conditions, communication...). But, there are still lines not to cross there. The Army is a mix of technical, skill trades and just plain 'grunt work'. A good all around service, but I'm somewhat biased.
The Marines take a lot of hits from the other services, but they are hard chargers and since they are a smaller service, tend to be more stringent and lower rates when it comes to promotion. That doesn't mean it's easier in the other services, but with larger requirements come relatively higher rates of promotion.
As for knowledge to have, once you pick the service, start learning some of the base line knowledge such as rank structures, common terms, service creed and ethos. If you can get ahead on those, you'll have a little less stress as you learn other basic knowledge.
Recruiter wise, ask to speak with either the detachment XO or Commander, then work on your contract.

The vast majority of officers serve in military occupational specialties (MOS) that do not directly align with their college education. After you complete your commissioning program, you will attend some sort of officer basic course that will train you in your MOS. So the answer can only be determined by what you want from your military experience/career.

There are so many permutations that it is difficult to give you a meaningful answer. Any general answer will have some absolute exceptions completely contrary to the advice we might give.

You must prioritize:
Geographic stability
Travel
Post-military skill set/career
Service "corporate culture"
MOS "corporate culture"
Physical nature of the work
Intellectual nature of the work
Danger
etc. etc. etc.

No matter which service you join or job you choose, you can rest assured that every part of the military is geared to entry-level training, no experience required. No assumption is made that you know anything at all about basic hygiene, rules and regulations, or even how to speak english. Everything is geared around the lowest common denominator. I wouldn’t worry too much about your lack of any prior experience. You should focus more on which service and job feels like a fit for you. The military will take care of the rest.