Which of the reform movements of this period (1829) do you think was most successful?

By the reform movements of this period (1829), I'm assuming you mean the various reform movements that may have begun by then but that gained strength in the 1830s and 40s, including movements that pursued abolition of slavery, women’s rights, temperance, and education reform. All four of these movements eventually succeeded in achieving their objectives, but not all at once—and not all would institute permanent change.
The anti-slavery movement achieved its most concrete success during the Civil War, when Abraham Lincoln issued the Emancipation Proclamation, which freed all slaves in territory then in rebellion, and later when Congress passed the 13th Amendment, which abolished slavery in the United States.
The women’s rights movement, which itself initially grew out of the abolition movement, took a backseat to the latter cause in the pre–Civil-War era and immediately after but finally achieved its goal of women’s suffrage in 1920, with the passage of the 19th Amendment.
The temperance movement, led by religious reformers, achieved some success in getting states to pass bans on alcohol by the 1850s but didn’t triumph on a federal level until passage of Prohibition with the 18th Amendment in 1920. Both Prohibition and women’s suffrage grew out of an era of Progressive reforms, but only women’s suffrage would stick, as the 21st Amendment repealed Prohibition in 1933.
The 1830s also saw the rise of the Common School Movement, which sought to establish a system of free public education in the United States for the first time. Led by Massachusetts lawyer and legislator Horace Mann, crusaders for public education across the United States spread the belief that elementary and secondary schools should be free and supported by taxes, teachers should be trained, and children should be required to attend school—ideas that came to be widely accepted by the time of the Civil War and are still in force today.