I can help you with the rating breakdown, as I wish I was more informed when I made the decision. I'm an electrician in prototype now, and chose my rate based off my interests. I worked as a commercial electrician before joining the navy and enjoyed it. It also depends on if you're on the surface or on subs. For you, someone who's planning to go officer, I would recommend MM.
If your degree is in mechanical engineering, or if you're interested in mechanical engineering, I'd definitely go with MM. They have a 3 month A-School, as opposed to the 6 month for "wire rates". Power school then becomes easier for MMs because they've already learned a lot of the subjects, such as HTFF. They also have the highest re-enlistment bonuses at the moment, tied with ETs. (I believe they're capped at roughly 100,000) If you decide to stay enlisted, you have the option to become an ELT which is a very interesting career path, but either way, mechanics work a lot on ships.
If you're more interested in the electrical side, what we call "wire rates" are probably more for you. I would definitely recommend you go ET. If you stay in, you'll be welcomed with the highest re-enlistment bonus. All your training is pretty much the exact same as EMs until you get to the fleet, and you'll get a higher bonus, therefore be paid more. ETs are also very undermanned, with the fastest promotion rate to my knowledge. ETs are also much more under the microscope though, they deal with very important, expensive components, and therefore are under a lot of scrutiny from naval reactors. Very stressful job, especially when ORSE comes around.
As for EM, it seems to be to be the even mix between the two. For the time being, the bonus isn't as large, but that's subject to change with manning. Electricians learn about running the electrical plant, and deal with stuff with motors, generators, and breakers. On subs it seems that EMs are the hardest workers, because they take the job of normal electricians as well as their nuke jobs. On a surface ships, all the Electricians I've seen get promoted quick, and really enjoy their jobs.
Really any rate you get, you will think it's the best nuclear rating. Nukes take a lot of pride in their work, and if there is anything else you want to know about the nuclear pipeline, feel free to PM me or ask on here. This forum has helped me a lot coming through.