To answer this question, we’d need to know more about what type of 19th-century American kid you were! Context is important here:

The privilege of universal public education is a fairly recent development, even in America. In 1850, regular school enrollment was still pretty low.

1850 statistics for all (public/private) American school enrollment for kids ages 5-19:

—White boys 59.0%

—White girls 53.3%

—Black boys “and other races” 2.0%

—Black girls “and other races” 1.8%

In 1869, there were only 2 kids receiving high school degrees for every 100 17-year olds in the U.S. population.

Even as late as 1870, Census data reported that around 11.5% of white Americans and 80% of racial minority groups in America were illiterate.

The total school enrollment figures for American kids ages 5-19 didn’t get above the 90% enrollment mark until...

—White boys: 1957

—White girls: 1983 (no, that’s not a typo)

—Black boys/other races: 1968

—Black girls/other races: 1971

So...as you can imagine, the response to the part of your question about what types of books you’d be reading & what you would be “expected to learn” would vary considerably depending on your race, sex, and class level.

As a general rule — Wealthier white boys would have been far more likely to see titles like “Beowulf” in upper/high schools, while many wealthier, white upper-school girls would have had to contend more with ‘feminine arts’ education & readings (manners, home care, lighter poetry, etc.)

Black, Hispanic, Native American and other minority kids lucky enough to get a full formal education in the 1800s were generally expected to work with whatever “charitable” texts were provided second-hand.

There were more than a few exceptions to these generalizations, of course, but overall it was a small, masculine, and very privileged group that would be expected to dig into challenging literary works or write analytical essays in 1800s American senior/high schools.

A few specific high school English text examples:

—The Girl’s Reading Book; in Prose and Poetry (1838) - Full text, Internet Archive: https://archive.org/details/girlsreadingbook00sigo/page/n3/mode/2up

—McGuffey’s High School Reader (1885) - Full text, Internet Archive: https://archive.org/details/mcguffeysnewhigh00mcgu/page/n5/mode/2up

—Sanders’ High School Reader (1863) - Full text, Internet Archive: https://archive.org/details/sandershighscho00sandgoog

Source for population data: “120 Years of American Education: A Statistical Portrait” (1993) National Center for Educational Statistics: https://nces.ed.gov/pubs93/93442.pdf

I've answered a similar answers that can provide some additional context. This one, on the shift of literature likely gets closest to what you're asking. And in this one, I get into the shift from the classical to the modern liberal arts curriculum as it relates to English class.

One thing to stress is how different education was at different points in the 19th century. /u/ModerateExtremism is spot on when they say it depends on who you are - but it also strongly depends on where in the country you live, your social class, your religion, your primary language, and your parents hopes for you and why they're sending you to school. Or, in the case of Indigenous youth sent to boarding schools, what the government wanted to you learn at school.

Also, the primary form of assessment for most of the 19th century was what's known as recitation. While English teachers in the later half of the 1800s raised concerns about how time-consuming it was to read students' papers, it was more common for a young person to participate in recitation. In some cases, they were expected to share or repeat back a specific answer the teacher was looking for.

The best source for getting a sense of English class in the later half of the 18th century across the country is to read the English (Modern Language) report from the 1894 Committee of Ten. The report is equal parts survey results and projections forward. So, we not only see what was happening around the country, we see what leading educators thought teachers should be doing. To cut to the chase (page 84):

The main direct objects of the teaching of English in schools seem to be two: ( 1 ) to enable the pupil to understand the expressed thoughts of others and to give expression to thoughts of his own; and ( 2 ) to cultivate a taste for reading, to give the pupil some acquaintance with good literature, and to furnish him with the means of extending that acquaintance.