Id say if youre worried about privacy issues, deleting your profiles from the console should be enough.
But, to clean out the storage space, you should go to Settings > Manage Storage and then delete all game data, including saves. You could alternatively delete local saves from the same Settings menu, one button down.
Then, just to be safe, you could restore factory defaults, the next button down in that same Settings category.
That will remove your games, your saves, and your profiles. Even if you just deleted your profiles though, your games and saved games would be inaccessible to a new owner without your gamertag and password.
Also, your data should sync to the new xbox one when you enter your profile data the first time. Id do some research though on games with saves that you really value, in case some games dont support that feature for some reason.