With ICS, the there isn't too many advantages of rooting.
Before ICS, you can root and then get Titanium Backup to freeze apps and do a backup of your phone. But with MyBackUp Pro, you can do a backup and ICS allows you to disable apps.
Before ICS, you needed to root to get screen shots but with ICS you just hold down two buttons for screens shots.
With root, you will have the ability to over/under clock your device but this can cause damaged to your device if you do something wrong. The other thing you can do is custom ROMs.
If you wanted to change they way your home screen looked, just look for launchers that fit your needs.
Since you are new to it, I would just keep reading on it and see if you need it or not. No need to root just to root unless you have a reason. Kinda like putting an empty bottle of NOS in your car just say you have NOS.