Just for fun. I'd like to offer you another option to consider, based on my experience and also a little bit of logic. If you want to see as much diversity in this great, huge country's geography as possible, I suggest the following:
- Cardinal and Zephyr to Emeryville/San Francisco, by far the most scenic route across the interior of the country.
- Coast Starlight to Los Angeles, in my opinion more scenic and diverse countryside -vineyards, vegetable farmlands, tortuous mountain pass, ocean coastline, space rocket launching site, and all during the daylight hours in summer. Added attraction, if you have sleeper accommodation, of the Pacific Parlor Car.
- Sunset Limited to New Orleans, a totally different feel of the American west because of the strong Mexican/Hispanic history and influences. (To my way of thinking, the Empire Builder and the SW Chief are too similar to the California Zephyr in scenery.) The desert landscape along the Mexican border can be spectacular, especially in dry climate where lightning storms can be seen flashing across the horizon at night. Besides, if you have, like many Frenchmen, a love for American jazz and great cuisine, you'll love New Orleans.
- City of New Orleans to Chicago, what I call the Woody and Arlo Guthrie train, up the Mississippi and through America's heartland south to north, a fine complement to your earlier east-west crossing.
- Lake Shore Limited back to New York.
You will have missed the southeast Atlantic region and the northwest Pacific region, but you will have gotten a taste of all the rest - especially if you have the time and money to enjoy stopping along the way.
I hope I haven't totally discombobulated your trip planning!
I agree with other commenters that, whatever route you take, you'll enjoy it.
