Performance wise, your Ubuntu "non-server" will run as a home server good enough without having to install or configure it, or even format it to put Ubuntu server on it.

I already did this 3 times, one in my own home, the other at a lan party place I go every so often and in my boss place.

There are little differences in performance between the server and desktop that you will notice in a lan environment.

My suggestion to save you time, money, patience is to just install the needed packages using the gui since it won't suck that much resources from the server. Which brings me to another point. Having or not having a gui will not have a big impact on your server (Specially for your home server). You will loose some memory which for a common 2GB or more ram PC is not even worth mentioning. It will not create problems and at the end, you will have a server that you can GUI manage.

Now, in what case-scenarios I would HAVE TO install the server version.

Well if you add to your question something like "I have a 32GB RAM server with 4 SSD drives and etc.. etc.. etc..". That puppy should better be a server version than a desktop version to use better the additional memory, cpu, drives, resources in general available.

Am assuming since you have used your PC for that much time is a common 4GB or less RAM PC with a common CPU and a normal hard drive. Just install the additional packages, don't give yourself so much trouble and time and enjoy your new Home brew server in which you can provide apart from the NAS and connection you want mentioned there many more server options that are generally available in the desktop (Like Web Cache with SQUID to speed up the internet for your family and network users, video sharing like VLC and more, folder sharing, printer sharing, etc..).