amoeba "kind" - Achaean period
amoebazoa - archaean eon.
and technically, there are no known eukaryote fossils from anywhere in the archaean eon, though it's likely this is when they evolved. really, we should list this as the slatherian era, in the paleo-proterozoic era, in the proterozoic eon, when we have the first fossils.
plant and fish "kinds" - Vendian period
plantae - ordovician period (paleozoic era)
"fish" are paraphyletic. technically, we're in one of the many "fish" groups. jawed chordates, gnathostomata, first appeared in the silurian period, also paleozoic.
arthropod "kind" - Pre-Cambrian period
"pre-cambrian" is a bad name, as it encompasses anything before the cambrian period, which is the vast majoriy of the earth's history. and in any case, hard parts first evolved in the cambrian "explosion" so you wouldn't see "true" arthropods before then their segmented worm ancestors.
primitive arthropoda - ediacaran period (neo-proterozoic era).
amphibian "kind" - Devonian period
kind of. amphibia does seem to first appear in the devonian, but the first "true" amphibians appear in the mississipian (carboniferous).
reptile "kind" - Carboniferous period
"reptiles" are polyphyletic.
sauropsida - pennsylvanian (carboniferous) period.
mammal "kind" - Triassic period
sort of. the first "true" mammals, triassic, as you say. but mammals actually diverge
lower than sauropsids from amniota.
ignorant creationist "kind" - Cenozoic period
homo - neogene period, cenozoic era.