That option above sounds great.
I'll provide some foundational details here, and recommend some questions you can ask if this is your goal.
ROTC: GPA, evaluations, the results of your physicals/ vision exam, scoring well on the ASTB-E exam (you get 3 tries, and take the last not necessarily the highest score), and tier of Major *look it up, all factor in to service selection and selecting as either a SNA (student naval aviator) or SNFO Student Naval Flight Officer. You should confirm - what factors into service selection for those going through OCS (Navy), OTS (Air Force), or PLC (Marines)? You should confirm if the Marines have guaranteed aviation contracts at-present for PLC/ ROTC. How does major factor in service selection/ getting an OCS contract? What does Poly-Sci and fly mean? All questions to investigate for you.
Opinions vary about whether or not a base level of flight hours is an advantage in the Navy for service selection and performance. One helicopter pilot working at a university NROTC unit said in no unclear terms - absolutely no advantage. However, at least as of last year, the service selection sheet did ask about prior flight hours/ certs. So I think it can help. I certainly advocate for getting up in the air for a free intro/ a few flight lessons to see how you like it/ if you like it - for sure. But, there is a lot of noise/ static from some that prior pilot training can be a risk for those who cannot adapt to the differences between the "Navy way" to fly and those training to fly commercial or sport or other aircraft. My position is - results, either from prior experience or other - speak for themselves and silence doubters. Terrible results only affirm doubts so it's pilot-specific. My other position is - try to find a flight instructor with prior military experience so they can train you both to pass the FAA check rides and for a career flying for the military - that's what my son did. But there will be counter-examples where a prior trained pilot is a terrible Navy/ AF pilot, too.
Are you certain you want to fly for an airline or commercially, even if the military doesn't train you to fly and you end up on a sub or whatever (do you want to fly after your service, regardless)? if so getting as many hours/ certs now would help so that when you get out, you're not spending 3 years or more earning your certs, teaching to then get ready. It's a hedge bet on yourself that few decide to make. DM me if that's your goal and I can explain further the options/ school parts, etc.
Hours/ certs before getting trained by the military? Generally, I wouldn't go beyond a private license with additional hours toward instrument before flying for the navy unless it's in a structured program that you can resume to be a pilot, outside of the navy, if you don't' service-select as an aviator
My DS is a CFI/ commercial rated pilot who is now a SNA, going through Navy's training pipeline- he is an Ensign. Before and just after commissioning, he has trained fellow ROTC midshipman as a flight instructor who are now with him as SNAs with their private/ some also with instrument ratings earned beforehand. Will this group with FAA certs do better or worse than the Navy flight students without prior training? I don't think any of them will fail NIFE (first phase of training). I don't think any of them will drop on request because in reality they don't like flying. I think they have a less-steep climb to learning the foundations of flight, weather, and will be quick to learn pre-flight because they know the basics/ what to look for and are accustomed to learning new checklists and following them. I think those with various airframes, like multi-engine ratings also have an advantage that may carry throughout the navy pipeline training as they understand/ have experience with that type of plane...
I didn't directly answer all your questions but within those details are nuggets you may find helpful as you weigh options and make your plans. good luck and thank you for your interest and willingness to serve.