My favorites are dirt rally 2 and assetto corsa. They are more sim like but still really fun and not too punishing.

Wheel makes the experience a million times better even if you just get a driving force gt for $60 (what i have used for 15 years)

If you just want to jump into something small, and single player. Super Woden Rally Edge would be my first suggestion.

Then from there you can decide what you want to jump in to next, more rally would be Assetto Corsa Rally, or Maybe something a little older like Dirt rally 2 or EAs WRC. Rally is probably the easier choice for controller if you want to start diving in to more sim racing stuff.

If you decide you want to look more into track racing, check out Raceroom as it is free and you can do a few weeks of their free multiplayer races(learn the tracks first) or some free stuff in single player, or you can grab something like Automobilista 2 on a sale for cheap, these are both pretty drivable on a game pad, but a bit easier to jump in on a wheel. Assetto Corsa and Assetto Corsa Evo are probably not great on a game pad to jump into, but pretty good options for driving on a wheel, with something like Le Mans Ultimate being the current multiplayer sim racing game of choice(not including iRacing).

If you decide that you want to stick to something more arcade, and controller friendly then Forza Horizon is really good and probably the best option. Gran Tourismo 7 is also a good option if you are only on playstation.

I actually had a lot of fun at first with FH5 in the exact same position. The unlocks flow fast and there's a ton of stuff to tinker around with and explore, and the racing itself is very beginner-friendly. The difficulty settings and assists are very granular and can be fine-tuned to suit your skill level.

I particularly appreciated that it avoided a linear progression system and didn't make you start off on the slowest cars and slowly work your way up to the good ones, as it'll give you some insane hypercars right off the bat. The upgrade system and vehicle tiering also ensures that the "slower" cars are never truly obsolete. You can drive what your like, and the game never punishes you for it (in singleplayer, at least).

However, once I got through most of the single player content available, I started to sour on it at a certain point. The constant drip feed of new content in the weekly challenges was fun at first, but felt like a chore after a while, and it definitely takes advantage of FOMO, as the new unlocks in a given week are exclusive to that week and can't be obtained anywhere else, unless buying them from another player at often exorbitant rates. They do re-run previous exclusive vehicles in the secondary challenges sometimes, but there's no telling how long you'll have to wait for a particular car to come around again if you miss it the first time.

So yeah, your mileage may vary, so to speak, but I did put something like 300-400 hours into it before I dropped it for good, and I don't regret most of that.

Need for Speed Heat and Unbound are decent, usually go on sale for dirt cheap. They are much more arcadey (which isn't a bad thing)

Forza Horizon is a great simcade experience imo. It's a good blend of realism and arcade style driving mechanics.

Dirt Rally 2 if you want to try rally style racing.

Racing games cover such a large variety of styles and levels or realism so it really depends what you like in a racing game.

There are proper sim racers but they are much harder to get into if you are just getting started (Assetto Corsa, iRacing, Richard Burns Rally to name a few)