Hi pocket,
It seems something is wrong on the whole vps setup.
Just to debug, put you as root user. Use something like:
$ cat /etc/passwd
To list current users.
If your problem is that you can't access mysql database, then your root don't have rights to it, try this:
mysql -u root -p
Then try again.
All that done, check if wordpress files have root or equivalent privileges only for the install, same for mysql/database. Don't forget to check your wp-config.php file too (redirecting to the right mysql database, on the right user, with the right permissions).
After you thoroughly checked that, logged off root.
Most installs on Debian/Ubuntu first create a user before install, then make it sudo for all things related wordpress - only for setup of course.
It's also possible that you created a linux user (for wordpress) that don't have rights to read & write the related mysql database.
Good luck on the debug, you can also check very good tutorials by digitalocean like this one:
https://www.digitalocean.com/community/tutorials/initial-server-setup-with-debian-8