Critical historical analysis requires the researcher to reconstruct the past by analyzing evidence. This evidence is found in written records, oral histories, artifacts, the enviornment impact and its impact upon an historical event. In addition, ancient and modern (urban) archaeology has played an essential role in the critical analysis of history. Remember historical analysis is always being tested by new evidence, assessments, and interpretation therefore choosing an event that has 'meat on the bone' will provide the best anaylsis criteria. I think the best way to choose an event in history is to first categorize events in what I refer to as 'managible chunks', in that way you might find yourself drawn to one over another....research that which sparks your curiousity!!! I've included several suggestions below.
1. How reconstruction shaped civil rights in the U.S. (1877-1960's)
2. The impact the industrial revolution had on American immigration. (1880-1920's)
3. How the industrial revolution and world wars changed the traditional roles of families and women. (1880's-1945)
4. How Progressivism influenced American politics. (1900-1912)
5. How WWI influenced U.S. foreign policy (isolationism) (1919-1941)
6. The 18th Amendment and the rise of organized crime in the U.S. (1920-1933)
7. How the failures at the Yalta and Potsdam conferences led to the Cold War. (1945-1989-91)
8. The Cold War and the rise of anti-communist fear in the U.S. (1950's)
9. NASA as a tool to fight the Cold War (1961)
Good Luck !!!