The comment about physical vs logical partitions is quite correct; you will be absolutely unable to implement the exact partition organization that you describe here, though you will be able to implement the functionality that you desire - the partition numbering will be different.
Personally, I don't see the sense in breaking all of the various system directories under / out into different partitions, particularly when they are on the same drive. There is no upside that I see, and the downside is that you limit each directory to a certain maximum size while also complicating your backup plan.
I personally would put / in one partition, with all subdirectories other than /home and perhaps /usr under it, and I would put /home and /usr on different hard drives - and different from each other as well if that were possible.
Since you are specifying all of these as IDE drives, I don't think there is much performance advantage in splitting things over multiple drives, but there would be some advantage. If the drives were SATA or SCSI (which is what I use) the performance advantages would be pronounced.
I do my backups using rsync and cron jobs.
My daily / backup cron script is this:
rm -rf /mnt/sdb1/back/backup6
mv /mnt/sdb1/back/backup5 /mnt/sdb1/back/backup6
mv /mnt/sdb1/back/backup4 /mnt/sdb1/back/backup5
mv /mnt/sdb1/back/backup3 /mnt/sdb1/back/backup4
mv /mnt/sdb1/back/backup2 /mnt/sdb1/back/backup3
mv /mnt/sdb1/back/backup1 /mnt/sdb1/back/backup2
cp -al /mnt/sdb1/back/backup0 /mnt/sdb1/back/backup1
rsync -a --delete --exclude /tmp --exclude /home --exclude /media --exclude /proc --exclude /sys --exclude /mnt --exclude /var/tmp / /mnt/sdb1/back/backup0
My daily /home backup cron script is this:
rm -rf /mnt/sde9/homeback/backup6
mv /mnt/sde9/homeback/backup5 /mnt/sde9/homeback/backup6
mv /mnt/sde9/homeback/backup4 /mnt/sde9/homeback/backup5
mv /mnt/sde9/homeback/backup3 /mnt/sde9/homeback/backup4
mv /mnt/sde9/homeback/backup2 /mnt/sde9/homeback/backup3
mv /mnt/sde9/homeback/backup1 /mnt/sde9/homeback/backup2
cp -al /mnt/sde9/homeback/backup0 /mnt/sde9/homeback/backup1
rsync -a --delete --exclude tmp --exclude .Mail/spam /mnt/sdd5/home /mnt/sde9/homeback/backup0
and on a weekly basis I run these two crons:
mv /mnt/sdb1/back/backup6 /mnt/sdb1/back/weeklybackups/"$dirname"
mv /mnt/sde9/homeback/backup6 /mnt/sde9/homeback/weeklybackups/"$dirname"