In the late 1700s, the fragile new government began to experience growing pains. Initially, there were no political parties, but as differences began to emerge about the formation of the centralized government and the proposed Constitution, the Federalist and Democratic-Republican parties formed. What were the major concerns of each political party? How did these opposing political views affect ratification of the Constitution and the addition of the Bill of Rights? Select one of the first ten amendments to the Constitution. Why do you think this amendment was included? How was it significant to the development of American democracy?

Before going any farther, I do think this question is posed a bit problematically in the way it conflates the first political parties which emerged under the Washington Administration (the Federalist Party and the Democratic-Republicans) with the Federalist Debates, which surrounded ratification of the Constitution. While we can assume an overlap between the two, they remain separate in contexts, surrounding different issues and political questions. This fact is well illustrated in the example of James Madison, who was among the leading supporters of the Constitution, as well as one of the leaders of the Democratic-Republican Party. Thus, if we were to look at the earlier ratification debates, he would be counted among the Federalists, but if we were to look towards the evolution of the first political parties, he'd count as a Democratic-Republican. With this in mind, a distinction needs to be made: when we speak about the Federalists and the anti-Federalists, and when we speak about the Federalists and the Democratic-Republicans, we are actually talking about two different things.
In many respects, I'd certainly agree that both sides of that distinction were shaped by concerns about the centralization of power (and its risks vs. its advantages). In the earlier Federalist Debates, the question centered around whether the new, more centralized government represented by the Constitution should be adopted at all. The first political parties, on the other hand, ultimately evolved within the context of governing within that Constitutional Framework. In this context, the Democratic-Republican Party favored the constraint of Federal Power and argued in favor of Strict Constitutionalism, while we might suggest that the Federalist Party, tended to support the opposite. We can then certainly see a connection (in that the entire post-Revolutionary War period was one strongly shaped by concerns about tyranny and the centralization of power), but even so, we're looking at different contexts, with one debate concerning whether or not this new system of government should be adopted and the other concerned with how politics should operate within a system which (by this point) is already being put in place.
In any case, when you select an amendment from the Bill of Rights and begin to analyze it, I'd suggest you think about the concerns which would have shaped the inclusion of the Amendment. Consider that, if a certain behavior is constitutionally protected, if there are explicit limits as to what the government can and cannot do, that means there must be a concern that the government might one day breach that right. Think on what this suggests about the concerns of the post-Revolutionary generations, and what they might be worried about politically. I'd also suggest you think carefully about the longer arc of US history and try to fit this amendment and your understanding of it within that larger context.