Weather can always be unpredictable, but usually the trains do get through. They tend to be subject to far less problems than the airlines.
As for sleep, no one can predict that. Many people, including myself, sleep quite well on trains. I always get a bedroom though, but I know people who sleep quite well even in coach. On the other hand, I do know people who don't sleep well on a train. It really depends on the individual. Sorry, but that's the best answer I can give you.
As for what to expect, expect to be late, as Amtrak runs at the mercy of the freight RR's. Amtrak does not control the tracks or the signals. Additionally, you can expect to take all of your meals in the dining car for free. Although tip and alcohol are not included.
You should also find coffee, tea, and juice in the sleeping car. An attendant who will put your beds down at night for you upon request and return them in the morning. You should expect to spend some time enjoying the scenery from the Sightseer Lounge car, with it's floor to ceiling windows.
Finally you may wish to check out
these hints & tips from On Track On Line.
If you have more questions, don't hesitate to come back and ask.
Ps. I'm moving this topic over to the Amtrak forum, where you will probably get more responses from other people.