Regarding whether or not to get a Masters - it seems to be a utility specific thing. My old utility did not put much of an emphasis on it, while my current utility does (and even has a ton of PhD's running around the site). Personally, I think a NE undergraduate is just as valuable (within the nuclear industry) as a non-nuclear BS with a nuclear MS.
One issue with a major like biochemistry is that it limits you more than a engineering degree does, as many of the technical support jobs at plant sites need an engineering degree. My utility has completely separate pay scales for engineers versus other technical staff.
As far as the SRO/Reactor Engineer issue, about half the RE's I know were licensed at one time (all as STAs) before they became REs. At most plants, becoming an RE is a learn on the job process, with someone with a NE background needing on the order of 2 years to become really competent.
Getting an SRO is great if you can do it, but it typically is an extremely selective process (at our plant, most license classes have only 1 or 2 engineers, and they're usually either future STAs or people being groomed for higher management).
The SRO opens you up for positions all over the plant, as most departments have need for a person with operating experience.
