A qubit is a linear combination of |0> and |1>, and a qutrit is a linear combination of |0>, |1> and |2>. I remember Scott Aaronson once suggested building QCs with qudits (or qu-n-its with n>2).

No, they're called qubits. It's literally a quantum-mechanical bit, in the sense that it's a superposition of the |0> and |1> states---i.e., a quantum state that returns a bit when you make a complete measurement on it.

There are also qutrits, which are quantum trits (superpositions of |0>, |1>, and |2>), "qubytes" (collections of 8 qubits), and so on.

This terminology is now 30 years old, and in probably thousands of books and tens of thousands of papers. It's not going to change.

The earlier name for "qubit"---the name that Feynman, for example, would have recognized---was "spin-1/2 particle." But while there was some resistance, I think that even within particle physics, condensed-matter physics, etc., they'd now typically say qubit rather than spin-1/2.

In any case, would you pronounce "qit" like "kit" or "kwit"? :-)

Sure it makes sense - a qubit is canonically a quantum spin system, which has two eigenstates, up and down.

What about superposition? Or is that not considered a 'state'?

They're states but not eigenstates. It's like the difference between RGB colour and greyscale. In both cases there are infinitely many possible colours, but in greyscale they're all mixtures of two "primary" colours (black and white) whereas in RGB they're mixture of four (black, red, green and blue).

In a qubit the infinitely many superposition states are all mixtures of just two eigenstates.

Thank you! This makes perfect sense.

A superposition is indeed a state, comprised of linear combinations of the basis states.

Further, (and anyone, please correct me where I'm wrong), the eigenfunctions (which could actually be called eigenstates) of an operator ARE the basis set, as they are orthonormal. (Right?)

One can justify the name using the fact that the state space is 2-dimensional.