As living in Branson we've traveled that route afew times. You really have two choices both end up on hwy 65. The more laid back, yet alittle longer is I40 through Little Rock and meeting hwy 65 at Conway. The part around Little Rock is not bad traffic wise.
The other route is hwy 64 out of Memphis to Bad Knob then hwy 167 to hwy 36 at Searcy then onto hwy 124 to hwy 65. This is a true ozark mountain driving experience. The road is great the scenery is great its a sit back enjoy whats around you. Very doable with many curves.
Good Luck