In the Policies and Positions section, we have dedicated threads for the Aboriginal, Aryan, Inuit and Métis People.
By and large, the appropriate name to use for a People is what those People prefer to use for themselves. In some cases, that may vary.
In the case of Whites, "White" is often the default term. However, this choice of names often has the unfortunate side effect of inspiring some idiot(s) to launch off onto a tangent of reducing race to "skin colour". "European" is often used as an indicator of origin, but in the present era, many Whites, particularly those in the Americas, have long since stopped identifying with their European roots and think of themselves rather as Americans, Canadians, etc.
"Caucasian" is problematic, as the term is still fairly commonly used in the West to indicate Whites... but in Russia, it is used to indicate non-Whites, as the Caucasus Mountains are now predominantly peopled by Semitic races rather than White races. Thus, the term is subject to unavoidable confusion.
"Aryan" is perhaps by far the most appropriate term to use, an ancient name tracing its origins all the way back to the tribe of the Alans, a People occupying the Black Sea region whence the ancestral Nordic people swept forth in waves from 5500 BC to around 500 BC, populating Europe to the West and Persia to the East. The name "Aryan" literally means "Noble"; these were a People who valued such traits as altruism, benevolence, compassion, courage, discipline, fidelity, honour, hospitality, industriousness, perseverance, self-reliance, truthfulness and wisdom. Certainly, such a name speaks to more integral aspects of a People than a mere skin colour, subcontinent, or mountain range ever could.
In the case of Aboriginals, many prefer to style themselves "First Nations"; however, much as "White" might imply too much emphasis on skin colour, "First Nations" implies a prejudice that they were the "first" Peoples in North America. In fact they have conquered what are presently their lands from other Peoples who occupied those lands before them. The term "Aboriginal" is perhaps no solution to this prejudice, as it literally means "ab origin" - "from the beginning". "Indian" is by and large a thoroughly useless and confusing term, as there is a land called India whose Peoples are rightfully called Indians. There is a popular myth that Christopher Columbus had believed he had landed in India when he first discovered land in the West; it seems rather more likely that he knew full well he was not in India, and that he had referred to the natives he met as "Los Sin Dios" ("The Godless") as they were not Christians, and that from "Los Sin Dios" we eventually got "The Indians".
"Native" is also a problematic term, as literally interpreted, it means anyone of any race who was born in the land they occupy. Technically that makes myself, a Scottish/Irish Celtic-Nordic, a "Native Canadian".
In this case, we will most likely simply default to referring to them as "First Nations", as in this era, that seems to be what they prefer to call themselves. "Aboriginal" also seems like a reasonable default name.
I grew up knowing the northernmost Peoples as "Eskimo". This however was derived from a name an Aboriginal tribe gave them; their own name for themselves is "Inuit".
The Métis are a miscegenant race born of the collision between Aryans and Aboriginals. While all other Peoples migrated here from elsewhere, Canada is their very womb as a People. The name Métis literally means "Mixed"; it is comparable to "Mestizo", the name for the mixed Spanish and Aboriginal People of Mexico. The Métis are predominantly French and Cree, although there is a Scottish element in some as well.