Does it make sense but more important, is it even possibile?
Or it is suggested (https://www.psicoterapista.it/) in this case to start from a new installation :-\ ?
Yes it makes sense. to- go to the current joomla & virtuemart.
Old versions are NOT secure.
WHAT I WOULD DO
I would setup a development environment.
take your current site, and upgrade it. joomla and vmart.
Then, I would take a clean install, and move your data over.
ALSO, YOU ARE GOING TO HAVE TO MAKE SURE URLS ARE REDIRECTED ETC.
IT CAN BE A LONG PROCESS
Tp upgrade or to build a new site is a deceision that really only you can make. I guess it depends on how many products you have, if you have a lot of registered shoppers who rpeatedly use the site and so on.
It is possible to follow an upgrade path to get to the latest versions, a process that can be greatly simplified by using the Daycounts migrator - http://extensions.virtuemart.net/back-office/import-export/virtuemart-migrator-detail
PRO mentions URL redirects, these are relevant if you have a large number of products featuring well on search engines. For many sites using Joomla's own redirect component is perfectly adequate, but again, that's you own choice.