Check this website:
www.tamaletrail.com
I'm not a big fan of tamale's but I've heard good things about Doe's tamales. Most "southern" resturaunts have tamales - but be on the lookout for roadside vendors. There are a couple of guys that sell them out of carts in Greenville - sometimes they set up outside grocery stores or gas stations. There's a guy that has an old bread truck that travels the south delta (greenville, hollandale, arcola, etc) sometimes as well. They're not very expensive in most places.
There are many "local" dishes in the delta. Too many to list - and mainly because I'm so used to them that I don't realize they're "mississippi" or southern dishes until I leave the South. Boiled peanuts, grits, and sweet tea come to mind. If you're in Rolling Fork, stop by Chuck's for a Chuckburger and a shake.
As for the best HWY - they're about equal. 61 is a better road to drive on but you'll see similar stuff on both of them. 1 will take you way out of the way in a few places - especially the southern part of 1 in Issaquena county - not much there - 1 incorporated town and less than 2,000 people living in over 400 square miles.
sd