QGIS is a very powerful GIS system. The deb packages for Ubuntu and Debian are not the latest so I'll install it directly from the repository. As this is going to be a GIS server, I'll also install the latest version of PostGIS.

At the time of writing the latest versions were QGIS 2.2, PostGIS 2.1 and PostGreSQL 9.3. Installation was very straightforward except for a nasty issue (which has affected me a few times now) involving a conflict between two libraries: libgdal1 and libgdal1h. We need to get libgdal1h from the Deb Jessie repo. So there are 3 repos to add.

Add Repositories

Following the instructions on the Postgres and QGIS websites, I added these repositories:

deb http://qgis.org/debian/ jessie main

deb http://apt.postgresql.org/pub/repos/apt/ sid-pgdg

deb http://ftp.us.debian.org/debian/ jessie

You can either copy/paste these into sources.list(or sources.list.d/your_file_here) or add them using Synaptic. I used Synaptic. There are also instructions for adding keys if you want to make sure the packages are legit (and it removes annoying error messages about not authenticated sources). Don't do apt-get upgrade with the Debian repo on because it could cause some nasty issues about differences between Mint and Debian (as I understand it, LMDE is sort of halfway between 'Stable' and 'Testing', so mixing anything not specifically required from Debian could result in wierd messiness).

Install

Using apt-get or synaptic, install the following:

qgis

postgresql-9.3-postgis-2.1

Clean Up

Use Synaptic or a text editor to remove the Debian FTP repository. Then you can safely apt-get update / upt-get upgrade.