I want to set GeoServer in a machine that will also be hosting a webpage (a web map) and a database (PostgreSQL with PostGIS). Map layers will be stored in the DB, published in Geoserver and served to the Web.
I'm between Fedora Server and Ubuntu Server, I use Fedora Workstation as my daily drive, so I feel more leaned to Fedora Server. However I'm still new in the field and this will be my first time setting up a Server, so maybe Ubuntu has more documentation and thus more easy.
A decade ago, I might have suggested Ubuntu because it seemed like a lot of the open source GIS development was taking place on Ubuntu. It ran fine on RedHat derivatives; it was just a little easier to get running quickly on Ubuntu. However, even then that was probably more true for QGIS and friends than the server side stuff.
Fedora and Ubuntu would both be perfectly adequate. Part of it depends on what makes you most comfortable. If you ever plan to deploy this for someone else, though, it's a good idea to find out what environment works best for them.
If this is primarily (or even partly) about learning, stick with the OS you're familiar with and concentrate on just learning the tools. If your primary interest is using the tools, you might go with the suggestion from @key -- begin with one of the containers. On the other hand, if you really want to know how the pieces go together, there is no substitute for installing those pieces (PostgreSQL, PostGIS, Tomcat, Geoserver) one piece at a time and fitting them together.
(Full disclosure: Xubuntu is my daily driver and Ubuntu server is what we use at work.)
I'm deploying this for my company, I started as an intern and got hired recently. I'm hired to do GIS job and I'm the only one with programming experience and interest. My boss used Linux maybe +10 years ago and he knows I use it and I'm learning to code, so he wants me to set up a webpage with a map that displays different projects.
I'm planning to do Postgis (postgresql) + Geoserver + Openlayers. I plan to learn as I do it but I also don't want to mess a lot as is not a personal project.
I'm comfortable with both, Fedora and Ubuntu (I used Xubuntu, Linux Mint, Ubuntu and OsgeoLive in the past but not as daily drivers), but I still feel that I have a lot to learn about Linux, code and GIS.