Which "ism" (conservatism, liberalism, nationalism) best exemplifies the period 1815-1870, and why?
I think it is always difficult to find a "ism" that characterizes a historical epoch as usually different "isms" battle to become the dominant one and therefore often co-exist at a given time. Your question also does not specify which geographical area of the world you are referring to, although I guess you are referring to the United States.
I would say that nationalism and expansionism certainly characterized the years of your question. The War of 1812 agaist Britain caused a rise in the national sentiment and the and in the ambitions to exapand the national territory. These were the years in which the West was opened also thanks to advances in transportation and communications. These were also the years in which capitalism and the free-market economy began to emerge as powerful forces in American life. Factories grew in size and number thanks to advances in the mechanization of labor and in the birth of financial institutions that provided invested capital for the industrialists.
Another important "ism" of the period was racism. Non-whites were still thought of as inferior and, in the South of the U.S., enslaved. These were also the years in which American-Indians were forced to assimilate to American society and saw their independence and their rights curtailed.