There is a USB installer for Mavericks, it doesn't work on the late 2013 MBP's but will work on yours.
So go to the app store, download the Mavericks installer .dmg (you may already have it). The USB installer will also reinstall the recovery partition and IMO is the best way to upgrade. You will need an 8GB or larger USB flash.
After a time machine restore everything should be as it was, sometimes Adobe software might need re-activation but that's about it.
This should help.
http://arstechnica.com/apple/2013/1...otable-os-x-10-9-mavericks-usb-install-drive/