This is always a difficult topic because racial and ethnic identities are so complex, sensitive, and dynamic: what are the best (as in the most precise and neutral) terms for "White" people? I've heard terms like 老外, 洋人, and 鬼佬. Do Chinese also say 白人? More precisely, I'd like to know any terms that could be used for anyone that self-identifies as "White" (could have origins in Europe, North Africa, West Asia, or any of their former colonies like here in America). Many East Asians have skin that is as light as any European's; would they ever self-identify with a term that could be translated as "White"?
老外 and 洋人 are the general terms for foreign people, not specific to white people. 老外 is more often heard in oral Chinese. In formal situations, 外国人is more likely used. 洋人 is a somehow out of date word, seldom used today. 鬼佬 has an implicit negative meaning, don't use it.
And yes, Chinese refers to white people as 白种人 or 白人. But the words are not often seen in self introduction. The Chinese are more interested in where people are coming from, like whether one is coming from France, India, or South Africa, etc. And I got to say this is not for foreign people only. When two Chinese met for the first time, the usual introduction often includes 我是山东人 or 我来自东北, etc.
My closer Chinese friends do use the terms 白人 and 白种人 neutrally in the same way we use "white people", but by and large I find Chinese people avoid these terms, and are set slightly on edge when I drop them casually into conversation. One friend told me she doesn't use 白人 because "听起来有种族歧视，不是吗?". Instead she and other Chinese usually use "美国人/法国人/英国人 etc." to indicate whiteness, but of course this can lead to some politically incorrect statements：
A: “你的朋友是华裔吗?” ("Is your friend ethnically Chinese?") B: “不，她是美国人.” ("No, she's American.") [actually she's both]
Or this one:
B: “是不是美国人和黑人之间发生过很多冲突?” ("There have been many conflicts between Americans and black people, right?") [as if the two are separate groups]
In both examples, I'm fairly certain that the speaker is using "美国人" to mean "白人". Most Americans would take offense at this definition, because it subtly implies that non-whites are not true Americans, even if the speaker didn't mean it that way. Ironically, it is the avoidance of the term "白人", not its use, that causes the political incorrectness.
So, to answer your question, I think "白人" or "白种人" actually is the most neutral term possible for "white people", despite the fact that it seems to make most Chinese people slightly uncomfortable. Neutrality aside, 老外, 洋人, and 鬼佬 all refer to all Westerners, not just whites. And I don't think any Chinese people would self-identify as "白人" because of their skin color, except jokingly.
the most proper and natural words are 白人，白种人，西方人. Other words like 白皮, 洋人 and 鬼佬 are more or less ironic or offensive. It would be a good idea not to use these words if you want to appear polite. In addition, 外国人 is an extensive word for foreigners, which is not necessarily negative but contains a sence of alienation. And 老外 is an emotional derived term for 外国人.
There is a term 黄种人 identifying Mongoloids but almost only used when making a comparison with Negroids or Europoids. Thus the short form 黄人 is a rather obesolete one.
I think I sometimes heared people say 歐洲人 (European) vs 美國人 (American) which sounds very neutral to me as well. It would be kind of the same, here, as we refer to people from either China, Japan etc. (who we don't know for certain about where they're from, but somehow their appearance gives it away) as Asians，亞洲人.
With European vs American it would be an indication of how many oceans someone is away I think.