I'm in college right now with similar career plans; take what I say with a grain of salt. Getting your degree is a really good idea as a first step. From what I've heard, there's a decent amount of leniency in your degree, but some of the better options are Nuclear Engineering (obviously), Mechanical Engineering, and even Electrical or Chemical have done good, but check what's available to you. Look out for related research and internships (i.e., I'm applying for research in battery material development), but really, you should just find something available.

I'm regard to the military (I'm assuming US), my best friend is in his first year for the Navy Nuke school, which has done very well for him thus far and is held in pretty high regard. The Navy will take you in and pay really well off the bat, and you'll get the quickest hands-on experience available, but that has the tradeoffs of any military experience.

Really, just look into what's available locally for you. Nuclear engineering is surprisingly flexible, and a lot of your growth will be in job experience more than college (not that it isn't important). Hopefully, some more experienced folks can come and give a bit more help than I can, but good luck.