The GT Sport demo appears to be fairly comprehensive, too. You'll be able to sample the career mode, quick race mode, paint and graphics editor, and the photo mode. Even better, you'll be able to make some progress that will carry over to the main game. Though there are limits, you'll be able to transfer some of the vehicles, credits, and custom paint schemes from the demo to the full game, giving you a little head start.
The demo is also completely free to download and play. You won't even need a Playstation Plus account to try out the online multiplayer in this demo. The full game comes out on October 17.