This is a huge question that could take books to answer. Any answer in this space will be extremely brief compared to what is needed. Let us look at a few of the ideas, traditions, and values that shaped our country during this time.
One of these was the idea or value of democracy. The United States was, of course, founded on the idea of democracy. During the time period in question, it became more and more democratic. For example, during the Jacksonian Era, the US came to have things like universal white male sovereignty and mass political participation.
Another idea was the idea of Manifest Destiny. This was the idea that the US was destined to extend its control over as much of the North American continent as possible. This idea led to such things as westward expansion and the war with Mexico.
Another idea or value, sadly enough, was racism. The US was also clearly founded on the idea of white supremacy. This idea underpinned the institution of slavery, which was of course basic to the way our country was up until the end of the Civil War. Racism also helped to bring about the war with Mexico and it informed our treatment of the Native Americans.
A final value was the general acceptance of immigrants. Of course, there was prejudice, particularly against Irish immigrants, but there was also a willingness to accept the idea that newcomers had a place in our country.
These are some of the most important ideas or values that shaped our country up through 1877.