Take either I-55 or US51 to Dyersburg. Take US 51 around Dyersburg & Union City, and up to Fulton, KY. Take Purchase Parkway (mostly re-labelled as I-69) to I-24 and Paducah.
You can cut off a lot of miles by getting off Purchase Parkway in Mayfield, KY and pick up US45 straight into Paducah. It's a perfectly good road.