Thank you for your answer, you probably right I should maybe focus on California Zephyr (with a train coming from NYC to travel coast to coast), it's already enough for a first trip and I could do a second depending of my experience
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At least, Los Angeles isn't far from San Francisco, maybe with the Coast Starlight I could finish the travel with this road on train including the Pacific view
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Two general points and a personal recommendation.
Travelling on Amtrak long distance (LD) trains is very relaxing if in sleeper and if end to end.
Travelling coach is or can be a lot of fun and extremely comfortable compared to European trains, but you are 24 hours a day with quite a few other people. We try to travel coach from time to time to remind us there are 2 Amtraks, and to meet a real mix of people.
Sleeper is whatever you want it to be, private and comfortable (roomette) or private and all the facilities (bedroom). We tend to travel roomette as the costs are a lot lower than bedroom which means we can afford to travel further for longer.
Travelling end to end means you don't leave any LD train for between 1 1/2 to 3 1/2 days depending on route. The pace of the trains, being fed 3 times per day, being able to lay flat to sleep and the motion of the train make it a non tiring journey.
It's also possible by travelling end to end to visit the cities you start and finish at, plus quite easy to visit places near to these rail terminals.
Understandably wanting to visit places along the way allows you to get to know the country better (although in my view you will learn more about America from meeting and eating with Americans on board an Amtrak train), but stopping along the way can be hard on the body. If you will stop along the way I would whatever your route fly into New York City (fabulous if you haven't been there, just like you see on tv), and fly back from Los Angeles (more to that place than meets the eye, or guide book).
If you want to see a very diverse America in one journey it would have to be end to end Amtrak, my choice for the first time would be this:
NYC (NYP) to Chicago (CHI) with the Lakeshore ~> CHI to San Francisco (SFC) with the Zephyr ~> SFC to Los Angeles (LAX) using either the Coast Starlight or an Amtrak bus to San Luis Obispo (SLO) then the Pacific Surfliner to LAX (have to admit this is my favourite journey in the US so I am biased towards this, it has such a diverse view of California and often directly on the Californian coast).
In LAX you can make a side trip to San Diego by Surfliner, excellent if you have the time.
LAX ~> New Orleans (NOL) on the Sunset Limited (past some of the best of the deserts of SW America, at times directly next to the Mexican border just a few metres away, then across southern Texas, through Louisiana to NOL where you will feel at home) NOL ~> Washington DC (WAS) on the Crescent (through eastern America which is different again). Washington is one of the truly great world cities with so much to visit and see. Fly back from WAS.
If you do all this and pace yourself by staying a few days at the cities you arrive at it should not be stressful for you. But you will have seen quite a few of the many types of America although you will hardly have scratched the surface.
This is a personal opinion, there are many many kind and helpful people on this forum with great knowledge who will offer opinions which are all worth listening to. Only you know what you need from such an eye opening journey, but be careful, travelling America becomes addictive!