For Contact Export/Import see this article and click on the "New" or Classic" tabs.
Import or export contacts in Outlook using a .csv file - Microsoft Support

You can save the CSV file anywhere you want. When you Import you will be ask to point to where you put it.

The two databases in Classic Outlook are PST files that store all of your data. If you decide to use Classic Outlook (instead of New) you can simply copy the PST you are using to your new machine and Open/Add it to Classic Outlook.

Open and close Outlook Data Files (.pst) - Microsoft Support