Based on this map, the three new slave states most important to American expansion and the growth of slavery would be:
Florida (1819) In 1819, the United States signed the Adams-Onis Treaty with Spain, making Florida a part of the United States. This treaty also established the border between America and the Spanish territory in North America. (See attached image: Courtesy of Wikipedia) When Florida became a state, it was considered a slave state.
Missouri (1820) Missouri was added to the United States in 1820, as part of the famous Missouri Compromise. This compromise allowed Missouri to enter the union as a slave states (since slaves were already there), but would maintain a balance in the Senate by admitting Maine as a free state. Also, the compromise drew a line, at the 36-30 north latitude, making the expansion of slavery legal only below this line. Essentially, this separated America into "slave" and "free" states.
Texas (1821) In 1821, a man named Stephen Austin led the first American families into Texas, which at the time, was still claimed by Spanish Mexico. Throughout the next decade, many Americans migrated into Texas and took their slaves with them. Texas had rich soil and the right climate for growing cotton, which was becoming an increasingly important cash crop in the South.