Was there some sort of measuring stick as to how much a dollar, or similar currency in other country, be able to purchase? Perhaps rolling in dollars were for the rich men and cents for the peasants? If not, why are there 2 different denominations and why not 1 single denomination?
... was there an ideal standard for what the dollar could purchase?
What you’re asking is essentially the nature of value and its measurement. This has been a hotly debated topic throughout history (and it still is pretty intensely debated, though the usually the debaters for any one of many of the sides at play today aren’t directly stating “value”, so much as they’re using terms in reference to exchange or compensation).
Plato and Aristotle are fairly early sources that delve into how things ought to be valued (or rather, the value we ought to recognize) and the nature of wealth. In Nichomachean Ethics, Aristotle explores the concept of what he refers to as “natural wealth” (human necessities) versus wealth or coin gained through exchange. He details that we require natural wealth and that unnatural wealth is ultimately useless in satiating our wants and needs (an example used is the story of Midas), but that a medium of exchange (money) may serve a role as it stands as representative of demand for goods/services wanted within society - recognizing the need for a pricing system. He compares and contrasts the efforts and products of builders and craftsmen, and states that the exchange of their services and goods will really only be efficiently accomplished once an equality is reached between the efforts expended in each producer‘s creation and the wants of the creation. (An example directly used is a description of the exchange ratio that would fulfill this requirement regarding a house, furnishings, and personal attire. Note that he is essentially stating that a home is worth some number of furnishings and that the money utilized is therefore just a means to mediate exchange.) This idea is really the formation of the labor theory of value - put briefly, that the value of a good stems from the labor required to produce it - and it is very foundational in a lot of economic thought. Thinkers such as Aquinas have echoed these ideas (Commentary on Nicomachean Ethics) and significantly later, individuals such as William Petty used this as a jump board when arguing the value of a land‘s rent in Treatise of Taxes and Contributions - suggesting it be the difference in the value found from an individual working land in a way that produced goods non-necessary (such as silver through mining) versus the value of the goods he’d have produced on the same land in order to sustain himself (such as cultivating wheat).
Adam Smith somewhat differentiated his view on value in Inquiry into the Nature and Causes of the Wealth of Nations, when he asserted that as exchanges developed and evolved, a good’s value stemmed from what it may purchase or be exchanged for (the exchange theory of value). Some contemporaries refuted this idea and claimed that he was incorrectly not accounting for the entirety of labor placed into the production of a good (from its very beginning to end) and that a good’s value was still commanded by the labor expended in its creation.
Going a bit further, you have individuals like Carl Menger and Leon Walras that argue that the labor theory of value is incorrect and that really it’s a reflection of the subjective theory of value with regards to wage payments, where the value of a laborer‘s labor is actually determined by the context of their labor and production capability. (At this point we are now in the early 1900’s and the division should be clear.)
The picture I’m trying to paint here is that the idea of what something ought to be worth in terms of exchange has been a rather fluid and not fully agreed upon thing.
Now into questions of currency and its use in exchange. From the above, it should be clear that while there was philosophical bickering over the nature of value, at least initially the idea of value being related to effort should be recognized. The more effort placed into production of a medium of exchange (say, the more difficult it was to mine and cast the metal used for a coin versus an alternative medium), the more value the coin held - the more labor expended it represented. This may be seen with early minted Roman coins where the value held by the minted coin exceeded the pure precious metal it was composed of. A more demanded service or good was expected to carry with it a higher compensation (calling back to Aristotle). Exchange markets became more complex and mediums became more representative of exchange power and scarcity.
TL;DR: The history is a complex one and the question encompasses a lot, but it could be thought of as others were viewing it. That is, the value and price of a thing is considered with respect to another thing (whether that be other goods, labor, etc.). It’s a comparative measurement in a dynamic system where things are consistently changing and evolving.
Disclaimer: Not a historian, but I am a grad student in Economics and enjoy reading books that cover the history of Economic thought in my free time. Mainly answered as I saw nobody else had. Hope I answered your question.