Many presidents in the early and mid 1800's demonstrate the level of upward mobility that was available in America at that time.
Andrew Jackson left his home state of North Carolina a practically penniless young man whose parents had passed away and found the respect and adventure he craved in the Tennessee militia. He became a military hero in the war of 1812 and ultimately had a career that culminated in the White House.
Abe Lincoln was the most famous president of humble means. He really was born in a log cabin, the son of a bumbling farmer for a father. He had to move several times due to land title disputes in Kentucky and Indiana and taught himself to read and write. He left home and took several odd jobs to earn a living and ultimately ended up practicing law and getting involved in local politics. Having no real military experience beyond the Black Hawk War, he poured over military strategy manuals and led the nation through the Civil War.
Garfield certainly belongs on this list of Presidents that rose from humble means along with less well know commanders in chief such as Martin Van Buren and Millard Fillmore.
Garfield was brought up in a log cabin in rural Ohio by a single mother. He spent his childhood working on neighbors farms to bring in some income to reduce the crushing poverty his mother faced. He learned to read in a wooden hut in village and borrowed as many books he could growing up. He went on to a local college and eventually became its administrator. He held the role of teacher, preacher, soldier and had many other occupations before he entered politics.
There's still far too much corruption and money in politics, however it's refreshing that so many men in America rose beyond the circumstances of their birth to achieve the highest office of the land.