Actually, if you want Google to automatically restore your apps after a factory reset and/or device switch, I believe you need to have the following options set:
Settings --> Privacy --> Backup and Restore:
"Back up my settings" and "Automatic restore"
You'll want those settings present on your old phone, plus you'll want to allow those settings when you do the initial setup wizard on the new one. If you do that, it *should* automagically reinstall most of your apps for you, paid or free. There are some exceptions to this, however, as I've had some of my apps be missing after this process, and on rare occasions have it not work at all, but in most of those cases it was an issue with a custom ROM, and not the stock OS. Also, if you have multiple Google accounts on your phone, it will only do the auto restore for the primary account that you initially setup on the phone, so if you have apps tied to secondary accounts, they will need to be manually re-installed as well.