italics - What are the capitalization / italicization rules for Betta fish?

I recently edited this question on Pets.SE regarding fish compatability. The original author used mixed capitalization of "Betta" fish, but did not capitalize "neon tetra".

The Wikipedia entry on Betta states the following:

There is often much confusion in terminology regarding these fish. Siamese fighting fish, B. splendens, are frequently sold in the United States simply as bettas. Fish fanciers are thus often unaware that, as of 2006, there are around 65 species classified within the genus Betta. A further source of confusion is that while the generic name Betta is italicized and capitalized, when used as a common name it is usually not capitalized.[4]

Yet, throughout the article and even the citation above, Betta is either lower-case or capitalized and infrequently italicized. I'd like to chalk that up to poor article editing, but ultimately this leaves me confused.

How should {Betta / betta / Betta} be presented within the context of the question I linked, and likely standardized for future site questions?

I'm asking here, not on Pets Meta, because the language subject matter experts are here.

Answer

(1) When giving the 'scientific name': (Wikipedia): The application of binomial nomenclature is now governed by various internationally agreed codes of rules, of which the two most important are the International Code of Zoological Nomenclature (ICZN) for animals and the International Code of Nomenclature for algae, fungi, and plants (ICN) for plants. Although the general principles underlying binomial nomenclature are common to these two codes, there are some differences, both in the terminology they use and in their precise rules.
In modern usage, the first letter of the first part of the name, the genus, is always capitalized in writing, while that of the second part is not, even when derived from a proper noun such as the name of a person or place. Similarly, both parts are italicized when a binomial name occurs in normal text. Thus the binomial name of the annual phlox (named after botanist Thomas Drummond) is now written as Phlox drummondii.

(2) When mentioning just the genus, but in the sense of genus (p-h-l-o-x or b-e-t-t-a say), your Wikipedia article still capitalises and italicises (Phlox; Betta) (eg 'all the Betta species; the annual phlox is a member of the genus Phlox that ...)

(3) When not using 'scientific naming' (though the words may be identical) use lower case and no italics (My oldest betta died last week; I never buy phlox).

Of course, it's not always obvious which naming style is more appropriate in a given sentence, and the choice may be somewhat arbitrary on occasion.

It may be easier to write a paragraph using Hyacinthus orientalis (of the genus Hyacinthus) and its common name hyacinth, where the distinction between scientific and common names is always clear, if not when to choose which.