Going by what you're saying, I would be inclined to suggest Debian Stable. It's exactly that; stable.
Through each versions life cycle you'll only get upgrades available that address security issues and the package manager is designed to not over write the local configuration. You'll be fine ssh-ing in every few weeks and running apt-get update/upgrade. Additionally, all administrative tasks and applications work over the command line.
All the applications that youíve mentioned are in the package repository. Some of the versions may be slightly older than in other distributions, but the principle if that they donít make it into stable release unless they _are_ stable and free of release critical bugs.
Major version changes are generally expected at about 18 months to two years. So that will greatly reduce the frequency at which you need come round and dedicate half a day to a distribution upgrade.
Of course one of the questions you need to ask yourself is what distributions are you used to? It might be easier to maintain Slackware if that's the one you use all the time. The time and effort dedicated to the initial install is directly related to the number of calls for help youíll get!
For youíre consideration;
The install guide
Some pros (and cons) for Debian
Hope that helps. But if you have any further questions feel free to ask.