If you were Chinese, you had (mostly) been excluded since 1882.
If you were Japanese, things were complex after 1907–8.

If you were anything else, you were not excluded as such in 1916

although there were many who thought you should be
if you were the eastern or southern European
that you increasingly were: Russian / Polish
Jewish    Italian    Polish    Slavic    Greek . . .

—and you could have been excluded as a convict
lunatic   beggar    pauper    polygamist    anarchist
prostitute    epileptic    contract laborer    mental defective
bearer of loathsome / contagious disease . . . : a growing list.

If you came after 1892, you probably (90%) arrived on Ellis Island,
where in 1906 you were still likely (99%) to be admitted,

but where, if you came in 1914, you might have been given
an intelligence test by Henry Goddard, the results of which
were inconclusive (and your chances of being excluded small)
but in 1916 you might (10%) have been marked X mental defect.

If you came in 1917, the new Immigration Act could have excluded
you for 33 reasons, and for the first time would have done so
if you could not pass a literacy test (for which Madison Grant
had lobbied) or if you came from an extensive Asiatic Barred Zone.

If you were admitted, you might have taken a train
from New York to southern Illinois, where you probably
would have worked in a mine, especially if you were Italian.