I'm unfamiliar with the Server Core setup... but can't you install these drivers as part of the Windows installation process?
Storage yes, but I'm unaware of a simple way during a stock install to include other drivers. The storage ones are requested, and necessary, during the install. Otherwise the installation location does not show up (unless you don't use VirtIO block devices.) You can definitely add the tools into an image, and there is probably a way to include Ethernet devices ahead of time, but I'm not used to the installation process to know where it happens.
I just select all 3 of the INF files and go... It's always installed everything for me, lol... Just point it at the folder for the right OS and 32 or 64 bit... (Note: This is the way I did it in Scale v4.3... I've not had a chance to use their newer stuff yet.
At what stage are you selecting them?
During the install process... the same place where you go when you're picking the storage drivers.
I rarely do modifications at that stage. Still, handy to have a simple option because a lot of people will get the install done and find that there is no networking and need to know what to do at that point. :)