Your other suggestions have been quite good and should be followed. My wife planned our first family vacation, a three-day visit to Vicksburg and Natchez MS. This was more than twenty years ago, and she still talks about the McRaven House in Vicksburg. Our tour guide was excellent and we both learned a great deal about life at that time.
http://www.mcraventourhome.com/

Since you should be going to Port Gibson to see the 20th Alabama Regiment's first battlefield, don't miss the ruins of Windsor Plantation. This NPS webpage describes it as the largest plantation home in antebellum Mississippi. The ruins were used as a backdrop in the Elizabeth Taylor - Montgomery Clift film "Raintree County" (1957).

http://www.nps.gov/vick/forteachers/upload/Windsor-2.pdf
http://www.portgibsononthemississippi.com/historic_district.html
http://www.virtualtourist.com/travel/North_America/United_States_of_America/Mississippi/Port_Gibson-821218/Off_the_Beaten_Path-Port_Gibson-TG-C-1.html

I have a Natchez list of must-see attractions if you're interested.