Moodle downloads server for releases has a link to older versions no longer supported.
You didn't dig deep enough!
https://download.moodle.org/releases/legacy/
On that same page each version download listed shows minimal requirements. The 2.9.x version has these:
Requires: PHP 5.4.4, MariaDB 5.5.31 or MySQL 5.5.31 or Postgres 9.1 or MSSQL 2008 or Oracle 10.2
Might want to map out and check each hop you plan ... upgrade notes and 'requirements' ... compare them to what you have access to/can do with your shared hosting at hostgator.
If this server is on hostgator shared hosting am assuming it's linux based therefore download the .tgz - smaller package for Linux. The zip is larger and perhaps best suited for Windows. I also assume whatever control panel you have with shared hosting can un-compress a .tgz.
Maybe one of these? ....
https://support.hostgator.com/articles/hosting-guide/frequently-asked-questions
https://support.hostgator.com/articles/file-manager-getting-started
https://support.hostgator.com/articles/file-manager-getting-started
Me thinks, however, with shared hosting, you will hit a wall concerning database before version 3.6.x.
'SoS', Ken