Well when I went through the beginning process, I remember having a choice of nuke rate, which later I found out wasn't true.

I don't know how it works now. I am pretty sure its still a number thing and they just fill them as bodies become available. That said here is a basic break down:
MM = Machinists Mate = Valve turners, bilge cleaners, machinery operators. You will never operate a reactor in this rate, regardless of what recruiters may tell you.
EM = Electricians Mate = wire biters. If its electrical, they own it and work on it. Operate the electric plant on the ship. You will not operate the reactor in this rate either.
ET = Electronics Technician = smooth crotches. They are the rate that actually operates the reactor. And besides that, they work on their own reactor controls gear and thats about it.
Which rate to choose?I don't know because like I said I don't think you really have a say so anyway. You can make your "choice" based on your attributes/aptitudes and how long you want to spend in school. MM A school is like 12 weeks. EM... well I forget how long it is but its greater than MM but way less than ET. ET A school is 6 monthsish.
Now, NONE of them at all in any way whatsoever give you a nuclear engineering degree, regardless of what a recruiter may tell you. In all honesty, navy nuclear power is extremely watered (AKA dumbed) down. You will not learn "real" nuclear or reactor physics... forget about quantum physics. However, it will give you a good basic understanding of the stuff. Thats not so say that the training pipeline isn't difficult. It will still be difficult for those with no background at all, but mostly from a time crunch standpoint. You have to learn a lot in a short amount of time... I think that is what makes it at all difficult.
As far as subs or surface that really is up to you. I was a sub guy and wouldn't have traded it for surface ever. There are pros and cons to both. What I can tell you is if you volunteer subs in boot camp you start accruing sub pay immediately and when you graduate the pipeline and get to your boat, you get back paid to your first day in the navy. So now a days thats like a 2000 extra bonus. What else did I like about subs? The small crew, the one single easy to operate plant, the smaller base (depending on where you go), the fact that your CO could be your drinking buddy and no one gives a crap, etc. What I didn't like about it (fast attack life) was the unpredictability of the schedule, the long sea periods, shit breaking left and right. Of my 4.5 years on the boat, I spend 3 years of it at sea... not all at once of course. And you never knew exactly when you were going out or coming back. But hey, I am glad I did it... but at the same time I am glad I have less than 200 days left.

I can't speak to the surface fleet since I have never done it. What I can speak to is they advance WAY faster than sub guys.
Well this is long but I hope it helps.
Justin