The national speed limit (with a few exceptions, such as the Northeast Corridor in spots and the Amtrak-owned right of way in Michigan) is 79 mph. You'll find that the DC to Florida trains generally do not run that fast; probably in the 60-70 mph region in rural areas. South of Richmond and north of West Palm Beach, most of the train lines are single tracked, meaning that your train will have to stop at red signals when a freight train in the opposite direction goes by (your train will be on a siding). The ride will be more comfortable for you if you get a seat in the middle of the car, as opposed to above the bogeys (wheels) at either end of the car. The passenger cars have substantial springs and suspensions, so you should not have too much side to side swaying (in contrast to VIA Rail's tracks in Quebec, which caused some substantial side to side shaking on the overnight sleeper between Halifax and Montreal I was on earlier this year).

I find that if my sleeper train experience is on the first day of my trip, I have trouble sleeping because I am truly excited about the sleeper train experience. If my sleeper is near the end of my travels, I don't have any problem laying down and nodding off to sleep.

Train travel is great. Enjoy yourself!