Haven't lost everything! Surely 1and1 doesn't prevent one from making a backup of the courses. Make course backups ... without users ... and download them to a local archive. Those can be restored to either 1.9.highest or a 2.
As far as local install of Linux (pic your distro) ... there will be a learning curve and while not impossible, are you ready to tackle it (might need that students assistance ... is that a bad thing? [not!])? Might ask other students (younger) if they to have some expertise on 'other' operating systems. One might be pleasantly surprised! One could also begin an 'Independent Study' program with such students - there's your future 'support' and 'local experts' as you yourself develop expertise!
Regardless of the distro chosen if one looks at the pieces that make up Moodle: Apache, MySQL, and PHP ... Apache and MySQL are 'faceless' ... ie, they do NOT have a GUI for configuring. PHP is scripting. So if one going after a distro of Linux for a reputation of their GUI desktop ... no advantage when it comes to AMP and Moodle specifically.
The 'advantage' of a good GUI desktop has to do with installing/removing software and keeping it updated. Whatever one does, don't look at a Linux box as if it were the same as Windows (which most folks have experience with). If your Linux server serving Moodle is accessible by LAN or WAN or Internet, one needs to keep the operating system up to date ... as well as the Moodle code (hint: git).
Which ever distro you choose, find a good resource for learning the finer points of administering. All distros have a site of some sort and there are tons of community sites one can use for references.
If you plan to install this once and forget it, then you might need to re-think. Not sure that Linux Mint (really designed for desktop use - not server) has what is called 'long term support' ...
On the Ubuntu side of things it does offer a long term support server version. Ubuntu 12.04.1 LTS for extended support.
So does CentOS (based upon RedHat Enterprise).
You are beginning a journey. Paths chosen might change, but one of the great things about Moodle is that it's transportable (once one learns how to backup a site) to any platform that can run Apache, MySQL, and PHP - including MacOSX Server!
'spirit of sharing', Ken