The event that occurred first: The Missouri Compromise
The Missouri Compromise was passed in Congress in 1820. It admitted Missouri into the Union as a slave state with Maine being added as a free state at the same time, to keep the balance of slave and free states equal. It also prohibited any future slave states north of the latitude line 36 1/2 degrees north of the equator in territories of the Louisiana Purchase, with the exception of Missouri (north of that line) being admitted as a slave state.
The other items:
Discovery of gold in California was in 1848.
Application for statehood by California was in 1849.
The Compromise of 1850 was (obviously) in 1850. As part of the Compromise of 1850, California was admitted to the Union as a non-slavery state.
The Spanish-American War ended in an American victory over the Spanish, and the Spanish were subsequently forced to cede the territory of Guam, the Philippines, and Puerto Rico to the United States.
