Well, there are lots of theoretical nuclear physicists! A theoretical physicist can be someone who studies theory in any number of fields of physics -- anything from plasma physics through to solid state physics -- there are theorists involved.
Broadly speaking, there are three "kinds" of physicist - experimentalist, theorist and computational physicist. They will have some field of expertise, and that may be nuclear physics. Hence - theoretical nuclear physicist. I myself am an experimental nuclear physicist. Nuclear physics is a really great field, you should totally join!
As to how many years of schooling, it depends on the country you are in, but in general: 3-4 years of a Bachelor of Science, 0-2 years of a Masters degree (which may or may not be part of your PhD) and 3+ years of a PhD program. In Australia (my country), it's 4 + 0 + 3.5 = 7.5 years on average. This is on the short end. In the US, you'd expect to spend a lot longer doing your PhD.
ETA: As to what classes - in high-school, take the classes that get you into a bachelor of science. If you want to be a physicist, you should take the highest level of mathematics you can, as well as physics. Chemistry can't hurt.
In university, you would get a physics major (or a theoretical physics major, if it's on offer. It doesn't matter too much), and take as much maths as you can fit in alongside. You want to do as high level quantum mechanics as you can. Some astro courses also can't hurt (there are a lot of applications of nuclear physics in astronomy). Then you'd apply for a grad program in nuclear physics.