What is the best 18xx game to teach someone?
I have 1830, 1870, 1856 and 1833. Of them, I think 1830 is the most suitable for new players. 

It contains the basics of the game:


Private companies
Track building
Route optimization
Company management
Stock manipulations


If you want a simpler game, you can ignore the private companies. Lower the starting money a bit if you like. I have played with and without privates and it seems to make no significant changes to the game.

If the stock market is too confusing, you can ignore that too. Just have one company per player. It's possibly wise to reduce the number of trains, else you never get rid of those 2 trains.

Most players run away from these, so no need to get a more complex game.

All 18xx have their own focus. I like 1856, because you can get away with mismanagement and get rewarded in the end (just like in real life).