[subject] + 甚至 + [verb phrase]
[noun] + 、[noun] + ,甚至 + [noun]
[clause] + ,甚至 + [clause]
甚至 adds the item that goes furthest, the one the listener wouldn't expect: "even". It comes last, after the ordinary items, and goes directly before what it marks.
It's common in writing and fine in speech.
The list builds up to the 甚至 item. Putting it first breaks the build-up.
甚至 often comes before 连…都 or 连…也, which puts extra stress on the surprising item.
Between two clauses, 甚至 says the second goes further than the first.
连…都 on its own, and 不但…甚至, have their own points.