As a current Navy Nuke, I'll put in my 2 cents:
If you really want to be a SEAL or any other Special Ops, Don't go Nuke. In fact, if you want to cross over to anything(other then officer), don't go nuke. The Nuclear field is perpetually undermanned(due the fact a lot of nukes don't do more then 6 or 8 years and quite a few go nuts and end up getting dropped) and other then failing out or getting kicked out, they won't let you leave. When you get to boot camp, you'll get to see a guy from Special forces who will try to entice you to try out and show you a video of them doing really cool stuff. And then there will be a big Flashing "Nukes Need not apply" on screen. Nukes also can't IA(Indiviual Augemetee) either(though if you want to fight on the ground, you probably should join the Marines or the Army). But if you want to go SEAL, you pretty much have to wait 6 years until your enlistment ends and then go back in and try out for SEAL(I know this because I have a friend I met in bootcamp and went to nuke school with me wanted to become a SEAL. Then he found out how hard it is to cross over).
Also, you don't really get to choose what rate you get. You get offered the choice of ET(operates Reactor),EM(Electrician), and MM(Mechanic) and put things down in order of preference. They'll take that list and then throw it away and give you the rate they need the most of at the moment. If you become a Mechanic, you have the option of putting in for ELT(Chemistry and RADCON). However, if you don't like what you got, you're pretty much stuck.
Nukes do get good benefits, with the ability to reach E5(and be eligable for Housing Allowance) early one of the best ones, because it gives you ability to live off the ship fairly early in your career(and believe me, you'll want to pretty. Sharing a berthing with up to 70 other people and hearing announcements over the ships intercom when your trying to sleep gets old fast). You'll also be set up to work in the civilian power industry provided you make it far enough.
However, you'll work for your money. There's the pipeline, which washes out some people due to the stress or just not being smart enough or getting in trouble. You'll learn the basics of nuclear power and then apply at one of two prototypes, niether of which particulary represents what you'll be going to. So when you finish, just dump it because you'll have to learn it all over again.
The first year on the ship(or boat) is tough because you'll have to work through qualifying different watchstations. If you fall behind in progress, you get to spend more time at work studying. You'll probably never have an inport watch rotation better then 4 section(you stand watch every 4 days), and god help you if you go to a ship being built or being refueled. Then you get rotating shift work(Work 7 days in a row with a day off in between), at which point you can pretty much say goodbye to your non-navy social life. It's really fun when you hear non-nukes complaining about standing watch once every 8 days and just have to resist the urge to punch them.
Sorry, I'm venting. If you want to ask more specific questions, go ahead and ask. I'll try to answer as best I can.
I'm just saying though. Don't become a nuke unless you want to become a nuke. The Money isn't worth it if you end up hating your life like so many people do(and you won't know until you get there). If you really want to be a SEAL, go into some other rate and work to be a SEAL from there.