Actually, I think I'm wrong because I wrote 中国人, which literally implies a person from PRC. I'm still learning Chinese in school and I didn't know how to say "people of Chinese origin" haha

This may betray my own ignorance, but I believe 中国人 is perfectly fine for describing oneself even if you are not from the Mainland, such as in my case. I've hung around plenty of 1st generation Chinese folk from Taiwan and conversation seems to still use 中国人 as a general term, not as something specific only to Mainlanders. I suppose if you really wanted, you could use the term "Han Chinese", but that is in fact more ethnically specific than 中国人.