I am a fan of the auto train. It takes about 16 hours but 8 to 10 them you are asleep. At least I am. I do the sleeper car. Best sleep ever. I can only recommend purchasing tickets early. It is not like airlines, the price goes up as you get closer to the trip.
I love having all my stuff in my car. It is only worth it though, if you are staying for longer than a week. Of course I work about 15 minutes away so I can also work a full day before going.
You can try Amtrak guest rewards, if you have hotel rewards points you can trade them in for Amtrak guest rewards points and get train tickets.