Being a prior enlisted will not necessarily make you a better officer. It will allow you to have a better understanding of the day-to-day life your Sailors lead, but being, say, a junior nuke ET or AV is not going to help you prepare an OPS brief or prepare a visual search plan. Enlisted Sailors are the technical experts, operators, and maintenance people...the officers are the managers, tacticians, planners, and policy makers. The jobs overlap a bit at the senior enlisted/junior officer level, but it diverges from there as you go more junior enlisted and more senior officer.
Additionally, your chances of getting into OCS at the 1-2 year mark are extremely small. Once you join the Navy, the primary factor determining your selection for commissioning is going to be your service record. Considering that you will still be in power school or prototype at that point and thus have absolutely no real operational experience if you go nuke (not sure with AV, but you're not going to have a lot of experience at that point even if their training pipeline is significantly shorter), your service record is going to be relatively meager. On top of that, you'd also be circumventing the entire reason you want to enlist.
Your chances aren't any higher with a degree, considering that you need a degree to be eligible for OCS. Your degree just makes you ineligible for the STA-21 program, which is the primary way enlisted nukes get picked up for a commissioning program during the training pipeline.
If you want to go officer, apply directly as a civilian. Enlisting for the sole purpose of becoming an officer later when you are already eligible and have a competitive resume is counter-productive.
I don't know why you didn't ask these questions prior to signing an enlisted contract, but there you are.
Some other things...
-There is no such thing as an "AV officer." Your DIVO will most likely be a pilot or NFO. Yes, the designator is competitive and the medical requirements for flight status are more stringent, as is the age requirement (27 vs. 29 with no prior service).
-The $30k/yr nuke pay is for nuke officers who sign a 3/4/5 yr contract past their initial commitment. The initial bonus is $17k...15 upon signing the contract, 2k when you graduate prototype.
-There are females in the nuke program, and up until recently they were restricted to CVN assignments. Enlisted women have not hit submarines yet, though.
-Joining the Navy for a civilian opportunity is typically not the best idea in the world. You are committing yourself to 4-6 years of a profession that is going to take a lot of time and sacrifice...that's a lot to give up just so you can come out the other end with a job.
Additionally, employers are usually looking for people with experience in the field; your experience as an AV, nuke, or officer probably won't help you much with a career in biomedical engineering, since you won't be doing any of that in the Navy and will forget most of what you learned in college by the time you get out in 4-6 years.
What you really need to be competitive in your field is a graduate degree and some lab/intern experience. Without that, your bachelor's isn't going to be worth very much. A commissioning program would offer a better opportunity for getting a master's via your first shore duty...not guaranteed, of course, but there are many options available provided you don't get shafted with an IA or Pentagon duty.
