Google+ will only backup your pictures and Google Play will remember your installed applications but not those applications data nor the system.
In all honesty the OP's best bet would be Helium - App Sync & Backup, Helium works for both a rooted and non rooted devices, the later requiring a PC application to be used every time the device is rebooted. Helium allows you to backup your applications data, you can even sync that data across multiple devices. Personally I see no point in the OP rooting just to create nandroid backups, I'm a root advocate but rooting for this reason is pointless. A nandroid is only needed if a user is modding, tweaking or flashing the system and the nandroid is a backup. Android isn't like Windows and unless your playing with the system, restoring a backup or a restore point isn't nessecary.