Considering the Apple mobileMe service will be discontinued on June 30th, 2012 (being followed by iCloud, that, unfortunately, does not include a web hosting option), I had to find a new location for my web sites.
After several evaluations, I decided to host everything at HostGator, probably the best hosting solution.
In addition to the www.livius.net site, I also migrated the ilegeul.livius.net blog from WordPress.com. For this I installed a multi-site WordPress instance; I tried to configure it as close as possible to the original WordPress.com, but some small details (like thumbs up, ratings) could not be preserved.
In the future I plan to also migrate the ilgthegeek.livius.net site, but this will require to either purchase the Enterprise theme, or find another acceptable one.
Having an unlimited number of domains and subdomains available, in addition to moving the http://www.livius.net site here, I also created a separate site for the previous instance of the web sites, the one that was hosted at ines.ro up to 2009, available now at www-ines.livius.net; similarly, the documents related to the AOPA legislative initiative from 2008 are now available at aopadocs.livius.net.
The process was slightly more complicated then expected, due to the differences in the way the purchased Enterprise theme differs from the one used at WordPress.com, differences that required some CSS tweaking.