TATY, thanks so much for your response. I am actually bilingual in English and Russian, so I am not learning these per se, but just trying to get a clearer understanding of what goes on in these cases.

The use of genitive & accusative with "хотеть" makes sense now, but you say that

"Ждать and желать can take the accusative or genitive. I believe there is a difference in the nuance of the meaning."

-- Do you know what the difference is? I don't think I could ever say "Я желаю тебе счастье" in Russian; I'd always say "счастья".

With the verb "to wait," I think both "Я жду поезд" and "Я жду поезда" sound OK to me, but I can't quite tell what the difference is.

If you have any additional comments, I'd love to hear them. Thank you again!