Hello Nuno,
Although there is a very straitforward process for doing upgrade from 3.2 to 3.2.2+ as there is no major architecture changes done in the Moodle system in above mentioned version.
It will be highly appreciated that you shall take complete backup of Moodledata, Code directory and database.
Once done, you can download the version which you want to upgrade your moodle system to. After that, extract the new version and copy the config.php file of the development moodle instance to the newly extracted directory. Check the settings and do the changes accordingly (database details, moodle data directory path and webroot path).
It will automatically start the upgrade upon visiting the URL on browser.
Note :- make sure that upgrade should be done in development server first. Do the testing and if you will find everything is working fine (if there will not be any hard coding in moodle files) then it will be suggested to upgrade the live server through the process :- https://docs.moodle.org/32/en/Upgrading .
Although it will take comparatively longer time but it will ensure that hard coding will not cause any problem in live instance.
Kindly let me know your opinion.