My children and I immigrated to America by plane.

Generally speaking, if you apply for immigration to the United States, the immigration company will help you with the relevant air tickets and flight arrangements. For example, overseas Chinese immigrants are like this. You don't have to worry about that. If you go by yourself, you can book tickets through some websites and arrange the time, mainly because of the time difference and local hotels. You need to apply for a visa first, and then book a plane ticket to fly there.