I can answer Jennifer's questions based on experience editing for
horticultural publishers (and lots of others).
All components of a species name (genus, species, subspecies, variety, and
forma) are italicized, but the interpolated abbreviations subsp., var., f.
are roman. In addition, when a subgenus or section is mentioned, though
this is not part of a plant's name, it is italic. Families and higher
taxonomic levels are roman.
Common names are roman. Depending on the style adopted for a given
publication, they may or may not be capitalized; I prefer the "down style"
where capitals are used only for proper names (e.g., California poppy).
Cultivar names are roman and enclosed in single quotes (and following
punctuation goes OUTSIDE the end quote). The names of seed strains (e.g.,
the lily seed strain Golden Splendor) are capitalized, presumably because
they resemble trademarked brand names, but do not take the quotes.
In regard to hybrids, there are some names such as Crocus x jessopiae that
cover all crosses of two particular species. Such names are italic and
separated by a multiplication sign, though in casual writing we usually use
the letter "x" instead of the mult sign. A lily hybridizer told me that
such names are rendered, in speech, by saying the mult sign as "cross."
On Jennifer's specific question about names of groups of irises, "bearded
iris" is a common name and is neither italic nor capped. "Oncocyclus
irises" is a problem because the name is that of a
section of subgenus Iris, and I would therefore capitalize it, but I would
not italicize it except in the phrase "section Oncocyclus."
One confusing aspect is how to treat taxonomic genus names that are also
common names, or are being used in run of text like common names. The rule
for English-language writing is that when the word is pluralized with "s"
("crocuses") or preceded by a word such as "a, the, these", it is lowercase
and roman. A genus name alone is italic only when preceded by "the genus"
or used without a preceding article (e.g., "Crocus includes species that
flower in spring and that flower in fall"; "Eriogonum and Acantholimon are
appropriate dwarf shrubs for the dry bulb garden").
I'm sure there are other questions to do with this area of style, but these
are the basic rules followed by most horticultural and botanical publications.
Jane McGary