So I played around for a bit and got my first bashscript up and running :)
Had to go through a bit of tar and gzip, mysql and rsync - but nothing I couldn't do with a few minutes of duckduckgo and the man pages...
So here it is:

echo "Starting the backup-process"
rsync --stats --update -a -r path-to/wpfiles/ backupfolder/files/
echo "Creating tarball"
cd backup
tar -cf "$(date +%y-%m-%d)_files.tar" files/*
echo "Zipping tar"
gzip "$(date +%y-%m-%d)_files.tar"
echo "Generating MySQL Dump"
mysqldump -u user -ppassword mysqldb >"$(date +%y-%m-%d)_db.sql"
echo "Zipping dump"
gzip "$(date +%y-%m-%d)_db.sql"
echo "Moving files into position"

This script copies all files form the wordpress installation to a specific folder, tars and zips them. Then a sqldump is created - everything nice and tidy :D

Next up is automation of this whole process, but I guess running it from hand every time I changed something suits my needs pretty well for now - so this can be postponed until I get funky again xD