From my past experience:

NFS Shift 1 -Track race.Most difficult racing title I've ever play with aggresive AI and difficult handling.Comes with superb graphics
NFS Shift 2 Unleashed-Track Race.Redefined version of NFS Shift..less aggresive AI and easier handling.Graphics a bit better and for my system run with less lag than NFS Shift
GRID - Track Race.More casual racing title.not so hard and you can actually rewind the race 10sec earlier if you fcuked up your car.Graphics nice but somehow too much bloomy sometimes.
NFS Hot Pursuit 2011 - Illegal Race.Easier than both Shift 1 and 2.Very fun race slamming patrol car and avoiding helicopter spike strip.And yes got Bugatti Veyron patrol car
TRACKMANIA-Hot Wheel styled race.A bit cartoonish graphic and very fun hot wheel like track.You can build your own too.

I dont have Gran Turismo series since i dun have a ps3,just a PC.You can try DIRT 3,FORZA MOTORSPORT,TEST DRIVE UNLIMITED.So your choice...