New non-retina 13.3" mac, will I get OS registered in the app store?
The first time you start up the system and log into the OS, you'll be prompted to create an Apple ID or connect to an existing one. That will register the OS as 'purchased' and enable you to do Internet Recovery or download the OS from the App Store.

If you're using a MacBook with the same OS as currently available on the new MBP you wish to buy, it may be possible to simply take the SSD out of your existing MacBook and plug it straight into the Pro. (This has worked with me in the past with taking an SSD out of a MacBook2,1 and putting it into a MacBook4,1.) 

As for having to purchase the OS again, Mavericks is free. Any app that you've purchased/downloaded from the App Store can be installed on new systems free of charge.