Taxonomy of commonly fossilised invertebrates

Although the phylogenetic classification of non-vertebrate animals (both extinct and extant) remains a work-in-progress, the following taxonomy attempts to be useful by combining both traditional (old) "and" new (21st-century) paleozoological terminology.
The paleobiologic systematics which follows is "not" intended to be all-inclusive or completely comprehensive. For practical reasons and relevancy, the below classification and annotations "emphasize invertebrates" that (a) are popularly collected as fossils and/or (b) no longer continue alive on this planet. Therefore, as a result, some phyla, classes, and orders of invertebrates are not listed.
If a non-vertebrate animal is mentioned below using its common, or vernacular name, the creature is usually a living, present-day invertebrate. But if a non-vertebrate is cited below by its scientific, taxonomic "genus" (in "italics"), then it is typically an extinct invertebrate, known only from the fossil record.
Invertebrate clades that are (a) "very important" as fossils (for example, ostracods frequently used as index fossils), and/or (b) "very abundant" as fossils (for example, crinoids easily found in crinoidal limestone), are highlighted with a bracketed exclamation mark [ ! ].
Invertebrate groups that (a) are now substantially extinct, and/or (b) contain a "large proportion" of extinct species, are followed by a dashed notation [ – such as this ]. But invertebrate clades which are now completely extinct are designated with a bracketed dagger [ † ]:
Domain of Eukaryota / Eukarya.
Sub-domain of Opisthokonta.
(opisthokonts / the animal-related kingdoms / the proto-spongal choanoflagellates, proto-fungal microsporidians, true fungi, and true animals
Sub-kingdom of Parazoa.
Phylum Archaeocyatha / Archeocyatha / Archaeocyathida / Archeocyathida / Pleospongia [†].
(includes fossil genera such "Archaeocyathus", "Cambrocyathus", "Atikonia",
"Tumuliolynthus", "Kotuyicyathus", "Metaldetes", "Ajacicyathus" and "Paranacyathus")
Phylum Porifera / Nuda / Spongia.
(quintessential true sponges / marine, colonial, pore-bearing animals / organized collar-flagellates / poriferans; today mostly siliceous) – "half" of all documented species of Porifera are fossils and extinct 
Super-phylum of Lophotrochozoa / Protostomia # 1.
Phylum Bryozoa / Ectoprocta / Polyzoa.
(bryozoans / moss animals) – "half" of all documented species of Bryozoa are fossils "and" extinct 
Phylum Brachiopoda.
(lampshells, brachiopods or "brachs," not to be confused with the hard-shelled marine mollusks below) – "99 percent" of all documented species of Brachiopoda are now extinct
Super-phylum of Deuterostomia / Enterocoelomata.
Phylum Echinodermata.
(echinoderms) – "72 percent" of all documented species of Echinodermata are fossils "and" extinct 
Phylum Hemichordata.
(hemichordates such as extant acorn worms) – "Less than half" of the documented species of Hemichordata are fossils "and" extinct