just create a directory
inside Hercules/sql-files
call it something like bak
mkdir ~/Hercules/sql-files/bak
(I don't know where is your emulator in the filesystem... so I made a relative path to users home directory...)
Next, dump your databases in that directory using a user with access to your database(s)
If you don't know such user or you don't have it, use root (Attention, not the system root, the MySQL root user password)
Then just dump database(s)
mysqldump -u root -p hercrodb > ~/Hercules/sql-files/bak/hercrodb_backup.sql
If you store logs in a separate Database you may dump that too:
mysqldump -u root -p hercrolog > ~/Hercules/sql-files/bak/hercrolog_backup.sql
then just archive your emulator directory with your backup inside of it
tar -cvf HerculesEmulator.tar ~/Hercules
I like to use SCP now you can use either SCP or FTP to transfer that archive to your new debian VPS
On the other side just unarchive it
tar -xf HerculesEmulator.tar -C ~
And Import files from bak directory in your extracted emulator
cd ~/Hercules/sql-files/bak
Import main database
mysql -u root -p hercrodb < hercrodb_backup.sql
import logs database if you have it in separate databases
mysql -u root -p hercrolog < hercrolog_backup.sql
And like Meko said install all dependencies and recompile...
After you successfully imported your database(s) and tested server is running just
rm -rf ~/Hercules/sql-files/bak
for a good measure....