JB,
There is no way to predict delays, there are simply too many things that can cause a delay and one never knows when and where you might get delayed. Hopefully everything will go well, but expect the unexpected. Finally remember that Amtrak will make sure that you get where you're going if you miss a guaranteed connection and bears all expenses associated with getting you there.
If you're going to be in a sleeper, I doubt that you'll encounter any lines for the facilities, much less long ones. If you're trying for the shower in the morning, you may find it occupied, but even then your wait shouldn't be that long.
Normal tip for a sleeping car attendant is 5 bucks per night/per person. Again use your discretion giving less or none for poor service or extra for outstanding service.
Also remember that all your meals are included with the price of the sleeper, when taken in the dining car. Alcohol will cost you extra, as will the food served in the cafe/snack/lounge car. The dining car attendants will also expect a tip, even though your meal is free. If you can figure out the total amount of your check, something not easy to do since you won't see your final check, then a typical 15% is customary. Most people however take the easy way out leaving a buck for breakfast & lunch and two dollars for dinner.
As for other tips, make sure that you spend some time in the Sightseer Lounge car with its huge panoramic windows. Bring a good book or other form of entertainment, should you get tired of looking out the window. If you're bringing any electronic equipment, tape player, DVD player, laptop, etc. then make sure that you bring a surge protector with you.
Keep in mind that the bedrooms are not huge, so watch the size of your suitcase(s). You may even wish to pack a small overnight bag with your clothes for the journey and check a large suitcase. On the trains west of Chicago, there is a large luggage rack in the lower level of the sleeper car. However east of Chicago, there is no rack, and there is only room for a moderate sized suitcase in your bedroom, unless you have a deluxe room.
Finally you may wish to check out
these hints & tips from On Track On Line.