This can be a good place to start looking: https://www.speedrun.com/games#title=racing
Heres an old school game thats pretty good it's called rock n roll racing for SNES. Like the above poster said need for speed those games are always fun!
https://www.speedrun.com/cmr - Colin McRae Rally Series https://www.speedrun.com/driver - Driver Series
I'd say Super Hang-On is great for a racer because the first course is only 6 stages, it's so accessible and short to reset between runs. All you have to do is get used to braking and being defensive of big offs or crashes, avoid big knocks into other riders, learn the game, and you can easily get halfway up the leaderboard and more. And the game challenges you to whatever highest level you want, with no mechanic more complicated than tapping the turbo button to keep your average speed, and giving you the option to play as you like - either weaving through traffic skilfully, or focusing on good technique in corners and letting the rest take care of itself. I recommend the Genesis version first since the frame rate is slower than arcade which can be a bit much for newer players.