Mint's software center instead? We will see.
Edit:
It will use App Grid a proprietary application written in python, so you can look at the code but don't do anything.
Congrats on installing GalliumOS. If you are new to Linux as well then the world really is your oyster.
Without knowledge of experience with Linux or interests, I would offer a these few suggestions:
1) Make use of the GalliumOS update tool and run it often to keep everything up-to-date and secure.
2) Learn a little about how to use the terminal. There are an endless number of tutorial around the web for this.
3) Learn to install programs with apt/apt-get as well as by using PPAs. A good start might be to install App Grid via PPA:
sudo add-apt-repository ppa:appgrid/stable sudo apt-get update sudo apt-get install appgrid
App Grid is a good, lightweight software center ideal for discovering programs you might want to try out on Gallium.
4) Learn to customize XFCE, your desktop environment with new themes, icons and panel features. Gallium does a great job of making the desktop look great, but its always fun to put your own twist on it.
5) If you have problems, don't be afraid to dig for answers. Usually, if you have a problem someone has already solved it and posted info somewhere. If you don't find Gallium-specific answers, generally info regarding Ubuntu, XFCE or Xubuntu will apply.
Enjoy.
> On Ubuntu and like systems there is Ubuntu store
Canonical has all but abandoned Ubuntu Software Center.
Ubuntu MATE has switched to App Grid. Other derivatives will probably move away from it also. Linux Mint already has had its own Software Manager for a long time (also used by various other distros). Perhaps GNOME Software will find a spot with Ubuntu GNOME.
GNOME Software is also usable on Debian IIRC.
> on Arch [...] I have seen people having problems with it
It works perfectly fine for me. It handles automatic updates as well. I have disabled that though, as pacman is much more informative (about .pacnew files, about new optional dependencies, and other such info you miss when doing automatic updates).
It will use App Grid a proprietary application written in python, so you can look at the code but don't do anything with it.
The Software Center is shockingly bad. There is an alternative that I haven't tried, http://www.appgrid.org/ and a new/replacement is coming up soon (not soon enough). Some people insist the command line is best, but it's only useful if you know what you're looking for. You can't really browse software in the terminal.