PhpStorm should use the same permissions as the user that runs/ launches the script (yourself). Add yourself to the www-data group, or set up a new group.
Let's say you created a new group called "www-pub" and added yourself to it as per instructions.
Remember to log out and back in to have the new group membership take effect. Test your group membership with the groups command.
Then, change permissions of the /var/www directory as follows:
$ chown -R :www-pub /var/www
Set the group of all files in /var/www to "www-pub" recursively
$ chmod -R o+r /var/www
Allows everyone (including apache) to read all files in /var/www
$ chmod -R g+w /var/www
Allows group members to write to all files in /var/www
$ find /var/www -type d -exec chmod g+s {} \;
sets new files to retain the group of the directory they are created in If you need apache to also be able to write files (or read files without giving read to everyone else), add apache's user (usually "www-data") to the "www-pub" group.
Also, in PhpStorm's Deployment Options, make sure "override default permissions on (files/ directories)" are either unchecked or set to allow writing by group.
This process should also work for IntelliJ IDEA/ Webstorm.