Recommendation: Backup system

[mo <mo777@gmx.net>]

Hi Debian users :)

Information:
Distributor ID:	Debian
Description:	Debian GNU/Linux 8.6 (jessie)
Release:	8.6
Codename:	jessie

As the title say i'm in search for a backup application/system.
Currently i manage my backups with a little script that i wrote... but 
it does not really serve my needs anymore.
I want to be able to make backups on my main PC and also on my server, 
the backups i would then store on my NAS.

Make a long story short:
Have you guys a recommendation for me?
Is there a specific application you use for your backups guys?

Btw: I dont mind configuring or playing around with new applications, 
every recommendation is welcome ;)


Here is my current backup script (Which is run by cron daily):
#!/bin/bash

TO_BACKUP="/home /etc /var/log"
BACKUP_DIR="/var/backup"
BACKUP_ARCHIVE="backup-`date +%d_%m_%Y-%H:%M`.tar"
TAR_OPTIONS='-cpf'

delete_old_backup() {
	if [ -f ${BACKUP_DIR}/backup*.tar ]; then
		rm -rf $BACKUP_DIR/backup*
	fi
}

create_new_backup() {
	tar $TAR_OPTIONS ${BACKUP_DIR}/$BACKUP_ARCHIVE $TO_BACKUP
}

main() {
	delete_old_backup
	create_new_backup
}

main

Greets
mo