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).
Being a flexible scientific investigator, I change my position so that each of these "kinds" were inserted at various points in the earth's history, as you have labelled. But I am going to contend that each kind insertion was a separate event, and that no two kinds evolved from one another.
this is where taxonomy would help.
"amoeba kind" as i pointed out above, is amaboezoa, in eukaryota. we're eukaryotes. "fish kind" is really paraphyletic. the largest group containing all "fish" is chordata, which also contains all tetrapods. we are chordates. amphibians are a subgroup of tetrapods, and we are a subgroup of tetrapods. reptiles are sauropsid amniotes. we are synapsid amniotes. and it should be obvious that we are mammals.
the problem with "poofing" each of these "kinds" into existance is that they are all on different levels of the heirarchy. many of them contain others that you are contend "poofed" into existance. and you are only representing a very, very minute sampling of taxa. nearly every group that you could even hope to name has a known ancestor -- the fossil record is actually quite smooth.
"poofing" things into existance makes very little sense, and indeed just becomes an extra arbitrary step over a much more simple and elegant solution. your idea, as it stands, already requires a fair degree of acceptance of evolution for one initial "kind" to produce all the variety of species under that taxon. why the added step, when that mechanism is more than adequate at explaining the initial member of the taxon?