One of the big things to remember about nuclear power is that the plants are only in a handful of locations around the US, most of them are rural areas (although major cities are typically an hour or two away), and on the east coast. Also, the entry level positions often don't pay for relocation, so you'd be on your own to get from where ever you live now to the area you want to work.
For education/experience, most plants want some combination of power plant operating experience and an engineering related degree (although any STEM degree might work) to get into operations. Neither are necessarily required, but that's what your competition will likely have. There are positions outside of operations that might be easier to get into, and once you get your foot in the door at a plant, it's a lot easier to get into operations.