Người is actually a classifier for people. There will be many classifiers. I'll write down the ones I can think of right now.
Con is for animals and children (and sometimes things in motion but that's more complicated),
cái is pretty general but pretty much for inanimate objects,
người is for people,
Bài is for compositions,
câu is for quotes, lyrics, etc,
tờ is for sheet like things (newspapers, etc),
quyển/cuốn is for books,
quả/trái is for fruits or round objects,
Good list to start with at least..