Before I go into a few "key variant" for a few of the languages, I will clarify a few things about my answer. Language is not nice and discrete - it evolves in time, and even in a given time and space, varies from speaker to speaker. Think of what I give as "key variants" not as nice discrete units, but rather a loose collection of similar trends and styles with very loosely defined fuzzy borders. Each of these languages has a lot of interesting variants, and I can only go into some in detail.
Hebrew
There are two different types of variation that go on in Hebrew. At any given time, the syntax of Hebrew users tends not to be too different, because most Hebrew users were in contact with other Hebrew users through extensive letter correspondences and book transmission even to very geographically separated communities, except when intentionally trying to emulate older versions, which happens a lot. In terms of pronunciation, very far apart communities had their version of Hebrew pronunciation evolve very differently. Ashkenazi Hebrew, Sephardi Hebrew, Yemenite Hebrew, Mesopotamian Hebrew all have different pronunciations for the same texts.
For time periods, even within the bible, there is a lot of variation between the oldest texts in the Bible and the later ones. The book of Esther has a style at least 4 centuries out of sync with the Torah (depending on how you date the books) and it shows.
Another big source of documents with a distinct style is Mishnaic Hebrew (found in the Mishna, which was compiled across the first few centuries of the first millennium CE). And after that, even though Hebrew was not used as a first language, the texts written in an active Medieval Hebrew showed some fascinating innovations.
In the late 18th C CE, you start seeing a new Modern Literary Hebrew emerge mostly in Central Europe. It is heavily tied to the Haskalah movement, which sought to emulate the European Enlightenment. Because its main use was in treatises and novels, it tends to combine rabbinic grammar, biblical flourishes, and styles borrowed from European novels, scientific works, and the like. This is not the same as Modern Spoken Hebrew, which arose more as a contact variety between multiple Jewish groups in areas we now would consider Israel and Palestine, and unlike literary Hebrew, is a first language for many people.
Latin
There are broadly three main clusters of varieties of Latin - "Classical Latin," "Vulgar Latin," and "Church Latin." There are preclassical texts that are clearly different than Classical (for example, the works of the playwright Plautus), and a distinct style that arose in the Renaissance. The most Classical works are from about the 1st C BCE, so that is usually the focus of Classical. It was the style people (especially those with money and ties to political power) wrote in, but not necessarily spoke as a day to day language. Because, especially as time wore on, later writers still wrote in a style emulating classical, while the spoken kept on changing, we refer to the spoken varieties as "Vulgar Latin," and there were variations within that, of course. Medieval Latin was not a first language, but was used as a medium of communication between different communities that did not share a language, and so still saw use and therefore linguistic innovations.
Arabic
Quranic Arabic is one form, and there is a "Modern Standard Arabic" that people learn in, but it is not the native language of most people who think of themselves as Arabic speakers. Modern spoken Arabics are very diverse, and frequently not mutually intelligible. Some large clusters of dialects are Maghrebi (Moroccan, Algerian, etc.), Egyptian Arabic, Gulf Arabic, Levantine Arabic (Syrian, Lebanese, Palestinian, Jordanian), Iraqi Arabic, and Sudanese Arabic. There also are (now mostly moribund) varieties of Judeo-Arabic, which tend to be similar to but distinct from the non-Jewish Arabic varieties spoken in the same regions.
Greek
Ancient Greek texts cluster into about 3 main varieties - Doric (the Spartan dialect was Doric), Aeolian, and Ionic-Attic (2 similar but distinct styles). Homer wrote in a dialect that was mostly Ionic, which was considered archaic by the time of Classical Athens writing in an Attic dialect. The interlanguage of the later Hellenistic world was Koine, and later works were in a distinct Byzantine Greek. Modern Greek is an evolution of Byzantine varieties.
Other languages on your list
All the languages you chose have many sources written over centuries in wide geographic areas, and the main point I am trying to make is that you can choose a lot of different "key varieties" and still miss out on important parts of their literary traditions. I think it can be useful to find clusters within the history, but horrifically reductive to think of the clusters you use as clearly defined monoliths. For your very ambitious project, I would recommend reading up on the histories of each of these languages in greater detail, to figure out what the right balance of capturing their nuances with a simple to code scheme.
