Memphis to Paducah KY

I-55 crosses the river at W Memphis, AR into Memphis, TN and goes south into Mississippi. I-55 North at W Memphis, AR heads toward Missouri, and, as mentioned has a spur I-155 crossing the Miss River to Dyersburg - divided 4 lane limited access ala interstate. Other option is to cross the river on I-40 into Memphis, and take US-51 north to Dyersburg. It is mostly divided 4-lane, but not limited access.

Also mentioned was US-45, again mostly divided 4 lane, but NOT limited access. You can take I-40 east from Memphis and pick up US-45 in Jackson, TN and head north.