Hello Lennart,

It would be best to install SmarterMail 15.7 on your new server, migrate everything over, then upgrade on the new server once you've confirmed everything is working as it should.  You can follow the steps in our kb articles Migrate SmarterMail to a Different Server and Major Upgrade of SmarterMail.

As for the server, 16.x and newer requires, at minimum, a Windows 2012 R2 64-bit or higher.  You can read the full system requirements in our online help here: SmarterMail System Requirements.  

Let us know if you have any other questions.