I know the nuclear industry best, so my answer is directed toward that industry. Oil and gas, other applications, I don't know.
The US nuclear industry is a direct outgrowth of the US Navy Nuclear Power Program. If you actually want to work at a plant, there is one way, and one way only, to get in. You must pass through the Navy Nuclear Power Program. Which means, of course, that you must be male. If this is what you want, enlist either before or after you get your degree as an Interior Communication Electrician for six years in the Nuclear Power Program, and volunteer for submarines.
As for the academics. A good program would be engineering physics with a double major in electrical engineering. Emphasis on the physics side would be transducer physics, including scintillator operation, GM tube physics, ion chamber physics, and fission chamber physics. Emphasis on the electrical engineering side would be linear and digital design, a whalloping big dose of software engineering, and a thorough grounding in real-time operating system. You might want to top all this off with an M.Sc. in nuclear engineering.
The market for these skills is somewhat tight in the US right now, but companies which do hire this sort of thing are Babcock & Wilcox, GE, Westinghouse, General Atomics, Gamma Metrics, Apantec, Canberra.
Good luck. Study hard.
- Catherwood.