I have been on iRacing for about 6 months. I wouldn't call it a game, definitely a sim.
If you want something to really enjoy all aspects of true racing style races, ie not the illegal street style racing you mentioned, then I would definitely say it is the best overall.
The only downside, is that it can get kind of expensive getting started on purchasing the cars and tracks that you want to race.
Overall, I think the quality of the variety of racing isn't be matched. At least not from anything else I have come in contact with.
They have everything from Indy, Forumla 1, Multiple levels of NASCAR, Le Mans, Skip Barber, Star Mazda, and so many more series as well.
You have to earn your license through Safety Rating (SR) to be able to progress to the next level of license.
If you would like to learn more about it I would be happy to talk with you in detail. There are tons of videos on Youtube as well for research if you like.
I do want to try GT6, but that is on PS3.
None the less, good luck with your search!