How to make an image of centos7 system on local media with schedule, exception, increments?

Question

Backup

There is centos7, it has two disks sda and sdb. sda1 is everything except /home. sdb1 is /home. sdb2 is /backup. I want to backup the system image with the exception of the /var/lib/pgsql/10/data/base directory and possibly incremental copying if there are tools for this. I want to shove all this into the schedule with further sending by mail and deleting old archives. In the open spaces I found tar, dd, rsync, cp tools. It is not clear which one should be used and how to combine.
For example, on the same server I do pg_dump for postgresql databases, but I do it clumsily, because it is not clear how exactly to send the pg_dump result to the mail, so I just send a message without the result of pg_dump itself, I do it through cron:

# get date
DATA=`date +"%Y-%m-%d_%H-%M"`

# loging
echo "`date +"%Y-%m-%d_%H-%M-%S"` Start backup base1c" >> /var/log/postgresql/myservice.log
# backup
/usr/bin/pg_dump -U postgres mybase | pigz > /backup/$DATA-mybase.gz

# loging end
echo "`date +"%Y-%m-%d_%H-%M-%S"` End backup base1c" >> /var/log/postgresql/myservice.log

# delete old backups older 30 days
/usr/bin/find /backup -type f -mtime +30 -exec rm -rf {} \;

# send mail notification
echo "$DATA"| mail -v -s "subject" -S smtp="smtp.mail.ru:587" -S smtp-use-starttls -S smtp-auth=login  -S smtp-auth-user="[email protected]" -S smtp-auth-password="mypassword" -S ssl-verify=ignore -S nss-config-dir=/etc/pki/nssdb -S [email protected] [email protected]

My current /etc/fstab is:

UUID=9321ed79-2d9b-4476-a196-5e5bad49776c /                       ext4    defaults        1 1
UUID=6ec4eac4-2de3-4436-9d44-8993e61ba957 /home                   ext4    defaults        1 2
UUID=28f8de93-2206-43db-99c6-b49d3fe6b34a /backup                 ext4    defaults        1 2

Current my fdisk -l:

Disk /dev/sda: 499.0 GB, 498999492608 bytes, 974608384 sectors
Units = sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 4096 bytes
I/O size (minimum/optimal): 4096 bytes / 4096 bytes
Disk label type: dos
Disk identifier: 0x000d5d24

Устр-во Загр     Начало       Конец       Блоки   Id  Система
/dev/sda1   *        2048   974608383   487303168   83  Linux

Disk /dev/sdb: 999.0 GB, 998999326720 bytes, 1951170560 sectors
Units = sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 4096 bytes
I/O size (minimum/optimal): 4096 bytes / 4096 bytes
Disk label type: dos
Disk identifier: 0x0004bb5c

Устр-во Загр     Начало       Конец       Блоки   Id  Система
/dev/sdb1            2048   419432447   209715200   83  Linux
/dev/sdb2       419432448  1951170559   765869056   83  Linux

blkid:

/dev/sda1: UUID="9321ed79-2d9b-4476-a196-5e5bad49776c" TYPE="ext4"
/dev/sdb1: UUID="6ec4eac4-2de3-4436-9d44-8993e61ba957" TYPE="ext4"
/dev/sdb2: UUID="28f8de93-2206-43db-99c6-b49d3fe6b34a" TYPE="ext4"