My cousin and I both graduated with chemical engineering degrees. I graduated one year before him, and I went off to Japan for some time, and just came back to America two months ago. I did not join the military. My cousin graduated a year after I did, and went into the navy nuclear program. He has finally finished all of his training, etc., and this coming Sunday his family is having a send off party for him, as he is now at the point where he has received his orders for where to be stationed (Pearl Harbor for him so he's quite lucky).
I would personally go to school before going into the program. I take it you are a high school kid, about to graduate? One thing to know is that recruiters will tell you anything you want to hear, even if it means lying or playing to your heartstrings. Don't trust a single thing they say.
If I were you, I would go to school first for a few reasons:
1) You can have the "normal" college experience, which I feel is really important. You may find by the end of it that you have zero taste for anything military related. It was one of the best times of my life, and there is no way I could have an inkling of what it would've been like had I not had that experience. You have to have that experience to understand it.
2) It will be MUCH harder to go to school after your time in the nuclear program.
3) Hinging on #2, even if you are in the nuclear program in the military and come out on the civilian side, you are still going to be severely limited for jobs outside of blue collar trades if you don't have/get a degree afterwards. Fact is, while jobs almost always have a preference for a veteran, if you wanted to go into something like engineering which I would assume to be the preferred/usual track for naval nuke people, without a degree you can forget it. This is the era where resumes are scanned by computers before people even look at them and when people do look at them, if they don't meet the very basic of the basic requirements, they go straight into the trash. No degree, no chance, at least in the engineering world, since that's requirement #1 on every single job posting in engineering; no military experience substitution, etc.
This said, if you go to school, get a degree in a related field, then do the nuclear program, like my cousin, you should be set up amazingly well when you come back into the civilian side. My cousin is going to be sitting quite pretty with a chemical engineering degree and the naval nuke experience, and he's not going to be limited to trades. He's going to have some serious weight to throw around for an engineering position when he's done.
4) Go to school first and find out what you really like to do, even if that means you have to pay for it. When I started school, I wanted to be a sociologist. I came out with two degrees much different than that by the time I was done--one in chemical engineering and one in chemistry. You may be interested in biology now, but who knows what you will be interested in in X years.
At the end of the day, if you go into the nuke program, you still have to go through all the petty military crap like having some powertripping asshat yell at you about trite things and scrubbing floors with toothbrushes at 5 A.M. Personally I can't stand that, and there is no way I could put up with some roid-raging jackoff like that yelling at me all day after the self-discipline it took to complete my degrees. That's just me though, sometimes I wonder how my cousin put up with that for the last two years, because he too is a smart, disciplined kid, not some screw-up off a farm in Mississippi. Just now my friend is getting to the point where he can start doing his work, but even then when he gets to his station he has to go through a ton more training, etc. One thing that is cool, is he has Top Secret security clearance right off the bat.
One other thing to consider is that you do what the military tells you and you go where they tell you, you have no say in the matter. You can't just up and decide one day that you don't like job A in location B and think job C in location D would be a better fit for you.
I get the feeling you just took this test for the hell of it, did really well, and all of a sudden are being pressured/harassed by recruiters, telling you how amazing you are and how they can groom you into this fabulous career in the military and how you don't need college. I'm particularly concerned because your tentative interests seem to lie far outside the realm of what the nuclear program is all about. The closest thing would probably be chemical/nuclear engineering, not biology. Even then, according to my cousin, it's still quite different, but he was thankful for the rigorous engineering coursework he took which teaches you how to think and approach things. I can confirm that because by the time I graduated, my approach to problem solving and logical thinking was completely different than when I started my degree. Thus, for him, he was at an advantage in the nuke program in that he already thought like an engineer, which takes time to learn how to do. Take your time and really think about this, because you sound impressionable, and this is not the kind of thing you want anyone else to make the decisions for you on.
If you're interested in the program, great, just make sure that you are actually interested in the program and the material itself, not what the recruiters tell you. The military is definitely not for everyone, my cousin and I are very similar in background yet completely different that way. He seems to be ok with it for now, I couldn't fathom putting up with it for more than a day.
But most importantly, however you do it, I would get a college degree be it before or after your time, for insurance if nothing else and how it will make you a better, more enlightened person. Just my opinion though.