On right-left politics: the terminology was born in the French Revolution, specifically the 1791 legislature where monarchists sat on the right side of the room and the radicals sat on the left. Since then, IMO, the use of the terms has steadily declined in value because big flashy labels do not help conversation the way calm specifics can.
Re early US "parties," if you are talking about the founding period and not the post-Washington republic, it is an anchronism, IMO, to use the word "party" to describe the groups vying for power. Even though they were laying the groundwork for our modern excuse for a party system, by endorsing the Constitution, they rejected the notion of "faction"quite explicitly (it's the only major gap in our original Constitutuion, IMO). You're also on slippery labeling ground when you try to call the Jeffersonians "liberal." Jefferson was perhaps the premier American exceptionalist, which is a stance that modern US self-described conservatives tend to claim as their exclusive point of honor.
before the late 18th century there was no school of political thought
Aristotle, anyone? Hamilton certainly valued his Aristotle, and most certainly understood that political theory was ancient and complex. If you're in the camp who believe Plato's Republic is serious and not a satire, and you put it beside Aristotle's Politics, then you've got a fascinating basic argument between healthy democracy and benign dictatorship. Heck, it works even if you laugh a lot when you read the Republic. And, if you're US-born, there's a strong chance you'll come out thinking that Aristotle would endorse our form of government as a very good compromise between the tremendous difficulty of mastering "good" democracy and the terrible risks of "bad" monarchy. Well, the formal form anyhow. We're effectively an oligarchy, which was the mediocre middle ground of gov't types in my reading of the book.
I should note that I sort of agree with SB about it being hard for us moderns to use our words like "republic" and "democratic" when we talk about history. But the real rub there is not about formal rules for assigning and using state power (for centuries, Venice was most certainly a republic in its own eyes--they elected their chief executive). It's the concept of citizenship that has changed most radically in recent centuries. For example, when the US was founded, most white men could not vote because they did not own sufficient property, and most of their wives were closer to the status of indentured servants than they were to citizenship--unable to own property or sign contracts, and often unable to protest a beating by their husbands.