Unless you are specifically going to Memphis, I would take I-55 at West Memphis, Arkansas.
You could go all the way up to I-57 and then US 62, OR
You could take I-155 over to Dyersburg, Tennessee, then I-69 up to US 51 at Union City, TN to connect with the Purchase Parkway in Kentucky/US 45 on to Paducah.
Either way will work. I am more familiar with the I-155/Purchase Parkway route.