Hi Shannon, welcome to the Amtrak unlimited forum! I've found people to be very helpful when I need information, and it seems to me you should get some great answers here, as each respondent will give you info from their personal experiences.
I am planning a trip to the southeast this coming winter, and I've found in my planning that it's kind of a cul-de-sac as far as trains go. Since Hurricane Katrina destroyed the trcks between New Orleans and Florida, you have to backtrack from that area all the way to Washington DC to get to Atlanta from there. Both Washington DC and New York City, on the other hand, are hubs, and trains go several directions from those cities. So, you might wish to consider flying in to Florida and starting there.
Another thing to consider is a
railpass. These are good for so many days/so many segments. A segment is a single train, between the time you get on and the time you get off. So it pays, if you want to see the wide-open spaces, to plan your segments so you spend as long as possible on the train between transfers and stops. But seriously, this is just about the best deal you can get.
You can also use the
Amtrak.com trip planner (where it says "buy tickets"), and go through several screens to see what your routing and scheduling options are, before obligating yourself in any way or entering any personal information.
There is no train service to Las Vegas, but I am sure there is a connecting bus. Unfortunately, if you are on a rail pass, even that short segment counts as a segment, but you may choose to pay for short rides as a separate ticket, and save your segments if you need them for the big rides!
Lastly, you can go to amsnag.net, and enter a starting station, destination (use amtrak.com to find the three-letter codes), and date range in order to find the possible routings and cheapest days for a given city pair.
Your trip sounds like a huge amount of fun! Trains are a great way to see the country and have a good time while doing so. Keep us posted and be sure and file a trip report so we can read about your adventures.