Your content is added to your Download List which is arranged in date order, with the newest first, so recent purchases will be at the top of the list.
You can remotely start the download from PlayStation Store on web browser by going to the 'Your New Content' section of the Purchase Confirmation screen or your 'Download List' provided you have switched on Automatic Update on your PlayStation 3.
You can check what content is currently remotely downloading or has completed downloading by selecting your Online ID at the top of the screen and going to ‘Download Queue’.
To download a game your PlayStation 3 needs twice as much HDD space as the size of the game. For example a 14GB game can only be downloaded to a PlayStation 3 with 28GB of free space on the hard disk drive.