In the beginning, there was…well, we're not really sure. The origins of language are lost to time. But at some point, there was Proto-Indo-European, the hypothetical reconstructed ancestor of all the later Indo-European languages. As the Indo-European people spread across the continent, the dialects they spoke started to diverge; one of these dialects (spoken in western Europe) became Proto-Italo-Celtic, then the southern part of that became Proto-Italo-Venetic (or "Greater Proto-Italic"), then the southern part of that became Proto-Italic (or "Lesser Proto-Italic").
But all of this, so far, is purely theoretical. Linguists have a pretty good understanding of what Proto-Italic looked like, but it's all reconstructed by comparing the daughter languages against each other—there's no actual written record of Proto-Italic. (Some linguists in fact only use the "Proto-" prefix for reconstructions: if we actually found some inscriptions in this language, it would be called "Common Italic" instead. But this convention isn't universal.)
Then, starting around the seventh century BCE, the situation changes. The Italic-speaking peoples have picked up writing from the Etruscans and/or Greek colonists in Magna Graecia, and inscriptions start to show up! So from this point, we have a pretty clear picture of what the different languages in the vicinity of Rome looked like: Italic had split into two branches, the Sabellic or Eastern Italic languages (like Oscan and Umbrian) and the Latino-Faliscan or Western Italic languages (Latin and Faliscan). And underlying all of them was a substrate of Etruscan, a completely unrelated language that had been spoken there before the Italic-speakers had moved in.
The Latin of the earliest inscriptions is generally called Old Latin, and is the oldest stage of the language that we have direct evidence for. Anything earlier, like Proto-Italic, has been reconstructed by comparing Latin and Faliscan and Oscan and Umbrian and so on to find the core similarities between them. And Old Latin, as a blanket term, covers everything from the Praenestine Fibula (seventh century BCE) to the mid-first century BCE. The oldest parts look quite a bit different from Classical Latin, but they're much more similar to Classical than Classical is to, say, modern Italian.
P.S. You mention Etruscan influence on Latin—there was definitely some influence, but it's not as huge as one might expect. The biggest effects I can think of are initial stress/medial vowel reduction and a bunch of loaned vocabulary, but not much else. Though it's hard to say for sure, given how little we know about Etruscan in general.
