Although you will be on the tracks of only two different railroads, it will seem more like four.
From New Orleans to Birmingham (the one in Alabama, not the one in England) the line is relatively straight and train speeds wil be in the 50 mph ot 79 mph range most of the time. It is single line and you will have numerous meets. South of Meridian, Mississippi, there are signals, but no CTC, so there may be the need to stop and hand throw the switches into and out of the sidings. You may have delays due to freight train meets, and will certainly see quite a few long freights.
Between Birmingham and Atlanta, the line is very curvey, running more or less cross-grain to the southern end of the Appalachian chain. Even though the maximum speed is still nominally 79 mph, for the most part the speed will be in the 35 to 50 mph range, with occasional short segments allowing 60 to 65 mph. Single track with quite a few freight trains. You may visit a few sidings here.
Between Atlanta and Washington DC the line was once all double track, but for the last 40 odd years has been about 1/2 double, 1/2 single in alternating segments of around 10 miles each. Due to increasing traffic and the desire of the state of North Carolina to run more and faster state supported trains, some segments of the second track are being restored. The last 40 odd miles into DC are still double due to commuter trains. It is in the middle of the night, but the recently restored Greensboro NC station is worth a look to give a picture of what once was normal in this country. the platforms there are new. The old station platforms have been long gone. Speeds on this segment will be in the 50 to 79 mph range, mostly in the 60 plus part of it. Quite a few freight trains, but mostly without waiting for meets due to the single-double set up. North of Atlanta the passenger loading is about double that south of Atlanta. A hint here: If you can, eat supper before getting to Atlanta.
At Washington DC the diesel will go away and be replaced by an electric. You are now on the ex-Pennsylvania Railroad northeast corridor. Generally three and four main tracks, except long sections of two tracks between Baltimore and Wilmington Deleware. Very few freight trains, but lots of passenger trains, well at least by US standards. Speeds will generally be in the 90 mph plus range. Do not know how fast they allow the equipment to go. 100 mph? 110 mph? Also, all stops north of Alexandria, Virginia are discharge only so the train is allowed to get ahead of schedule.
American Freight trains: If you have only seen English and continental freight trains you will have a shock. Picture 10,000 ton plus trains of 100 cars or so pulled by 2, 3, or 4 diesels. Much freight in the country now moves in containers on rails, two high. They tower over the single level passenger equipment. NS usually limits freights to 50 mph.