What is the right way to backup my whole phone?
If you only want apps/settings backed up, I recommend Titanium Backup.  It requires root.  Its backup will be saved to /mnt/sdcard/TitaniumBackup/, you can copy that folder to your computer just in case your card gets formatted.

If you use ClockworkMod / nandroid, do the same thing (copy the /mnt/sdcard/clockworkmod/backup folder to your PC afterwards).  The only real caveat is that you should flash the ROM you had when the backup was done before restoring the backup.  If the ROM you flashed afterward was significantly different, restoring without first reflashing the previous ROM can brick the phone.