Take it from someone who has driven from Starkville to SE Missouri several times... if you live on the east side of MS, go up 45 through Corinth to Jackon, TN and then cut across to Dyersburg, TN and get to I-55 in Caruthersville, MO.
Once you get to MO, the quickiest route from SE Missouri to Kansas City, MO is to stay on the south side of the state and drive to Springfield, then go north to KC (this will take about 6 hours from Caruthersville to KC, maybe a little more). It will take 7 hours from Caruthersville to KC if you go I-55 to STL then I-70 across.
From KC to Omaha, I've got not help.