Before anyone could provide you any info/tutorial, at the very least, platform of new hosting (Linux? CentOS 6 or 7, Ubuntu) Windows? should be shared.
Generally ...
Does TMD have a tutorial for their customers? Many hosting providers do.
Don't use any hosting offer for scripted install of a moodle. You want to migrate your site.
See: https://docs.moodle.org/32/en/Moodle_migration
for overview and how-2 ...
Prepare new hosting environment for versions of PHP, MySQL/MariaDB you need.
Moodle 3.2 has raised the minimum required PHP version to 5.6.5 - but might consider, since you are on a VPS now, installing at least PHP 7.0.x.
Your first challenge might be making a full site backup with current hosting. You need a tar ball of the code directory, a tar ball of the moodledata directory, and an SQL dump of your database.
If you have shell access on current hosting, you could use scp to transfer those files to the new host.
Will you be moving the current site fully qualified domain name to the new hosting server? If so, think I'd begin there ... getting DNS changed to point to new host. Makes it easier to xfer your current site to new host and install.
'spirit of sharing', Ken