If you want to know more about what you're getting in to, I recommend doing some reading on the background/history of NR/NNPP. Search on "ADM Rickover" to find some good books on Amazon. I'd ask why you're so "gun ho" for working at NR when you seemingly know so little. (You'll be in the Navy, but NR is actually a joint DOE/DON Program). There are plenty of nuclear engineering jobs available...in the Navy, DOE, and Commercial. Right now is a GREAT time to be an engineer looking for work. Why limit yourself to one of the highest areas for cost of living? Cast a wide net and have fun with the nuclear job search. You can also get more information on nuclear engineering job descriptions via the federal government job database.
Quotas? Everyone has billets to fill in the Navy, and Corporate world. Some are looking for a very specific skill set (for example a Professional Engineering license). If you do very well during your interviews, NR (or anyone for that matter) will likely find a job for you somewhere.
The interviews are technical, but the questions are designed to throw you off balance and be forced to answer under stressful conditions. (Welcome to Nuclear Power). You can't study but you can mentally prep yourself.
What you wear to work is irrelevant and what uniform you wear has absolutely nothing to do with being an officer (anywhere you go). The people that wear their rank on the coller but are technically challenged are normally limited by promotion boards and can't lose their Ego when they go to leave the Navy. Don't watch "Top Gun" or "NCIS" and then bring those misconceptions into the Nuclear Navy Program. Also, the work at NR is highly unique and the officers don't follow the normal "sea/shore" rotation that most "regular" officers will do. In fact, officers and civilians work side-by-side...all wearing civilian clothes doing the same job. If you compare Commercial Nuclear Corporate jobs to NR jobs, the NR job combines corporate leadership, INPO, and NRC regulatory oversight into one role.
While I disagree with NukeLDO diminishing the NR role in that NR Engineers are "a dime a dozen" and that "you're not leading people", any "staff duty" on any ADM Staff (SUBPAC, AIRPAC, etc) is very unique and highly challenging. However, being an Ensign is the same anywhere...you have to learn the ropes, get qualified, and figure out what your job really is before you're effective. (Usually by the 5 year point when you flow to LT/O-3). You may lead a small group of engineers at NR (eventually), but you also provide technical oversight for field personnel within your area of oversight. I would say that the same holds true whereever you may end up in that you start as an entry-level engineering, prove yourself, gain more responsibility, and then get promoted "up the ladder".
Good luck.