Derek, after looking at the hosteurope's website thoroughly I am somehow convinced that their basic and medium packages will not be able to install Moodle, as Moodle require innoDB and this starts at their premium packages.
also they have mentioned something like "WebPanel", have they not given you access to your hosting webpanel? as like I had mentioned before, CPanel/Plesk etc are names of web administration panels that makes the task of setting up things easier at user's end, and they are not just two, there are many more with different names, but all work to make things easier (setting emails, websites, installing scripts etc).
you can always ask them if the basic package can support "Moodle" as by looking at the specifications, it does seems to me that package is just for someone creating a small database driven website to test.
if they do not cater for Moodle installation on this package, try upgrading, else do give a try to contabo.com (contabo.de), they are German based too but a very recommended company.