Use Setup Assistant to restore from your backup. Quit Disk Utility, then re-install the OS. Reformat the drive using Disk Utility/Erase Mac OS Extended (Journaled), then click the Option button and select GUID. Boot to the USB Volume (hold down the option/alt key during a restart and select the USB). Do a backup, preferable 2 separate ones on 2 drives.
You can make a bootable USB stick to install using this free program which will do all the work for you.
