As for the first part, I suspect it doesn’t exist right now.
Project Cars 3 and something like the most recent GRiD feel like genuine attempts, but the core to a racing game is the racing and when a game drops a player into a race with low lap count and puts you in 12th place it’s usually an admission that the racing part isn’t actually very good.
It’s like a racing game version of the Chick Parabola. The intent is you fly around with your hair on fire trying to find a way past 11 cars in three laps in the hope that it’ll all be so hectic that you won’t notice that the AI doesn’t know how to drive. At all.
At the other end of the spectrum are games like the rFactors, Automobilistas, Assetto Corsas, Raceroom Racing Experience and it’s hard to recommend them because I suspect they’re aimed at a completely different audience and none of them offer a Pokemon style “collect 'em all” experience.
If I did have to pick one of these traditional sims I would go for the original Assetto Corsa.
Firstly it’s now frequently very cheap for the complete version with all the DLC so you’re out about $10 if the experiment doesn’t work out. Also it does have something pretending to be a career mode, although this is really just a gated series of events where winning one season will progress you to the next. It also has a fun collection of slow cars and the AI is fine.
All of those can be played with a gamepad, but a wheel will make a vast difference to consistency.
So my real choices for people coming from racing games who want to dip a toe into something more about racing would probably be:
Forza Motorsport 7
Has a large car catalogue that you can unlock and or buy with currency earned by driving and has some structure to offer, progressing through certain "Cups’ that limit car type and power.
The AI is fine and some powerful cars are controllable without using a wheel. It isn’t for everyone, but I have a soft spot for this game.
The downside is you have to use the MS store which is a nightmare and as with a lot of the games I play there isn’t much structure. A lot of the fun will come from thinking “I feel like racing these cars at this track” and then setting up that combo yourself.
Formula 1 2020
The official game of the Formula 1 world championship lowers the difficulty of driving the cars to appeal to a mass audiences and has a career mode where you progress from a (thin) Formula 2 season into Formula 1, develop your car and advance your way up the grid to better cars.
F1 has a lot of widgets and greeblies, but you can set the game to control things like engine mapping, DRS and energy deployment and never think about them again.
If you’re prepared to try riding a bike with a gamepad these games are a really good time. The AI is good and the career mode is excellent. In 2019 you can start in the Red Bull Junior series where everyone has the exact same tech, but in 2020 you’ll need to start in Moto3, then advance to Moto2 and then MotoGP.
I have had many of my best offline (single player), races ever in this series, because the lower power bikes are very slipstream dependent which means you end up racing in a pack and will struggle to escape the AI. This comes naturally without the devs having to put in some sort of artificial rubber banding.
The career mode is good for feeling like you’re making progress as a rider and you get to improve your bike as you go too, unlocking development points by meeting goals and targets in the practice sessions before races.
The lines through corners and braking approaches you take on a bike are very different to that in a car and the game hurts itself by having one of the worst “suggested lines” in all racing games. It turns in too late and brakes in wildly incorrect places so if you’re new it will actively hinder your enjoyment. It feels like a big step to turn it off, but it will really reward you to ignore it.
I was a real European snob about “circle driving” before I accidentally ran a Rookie Oval race in iRacing because my regular road race wasn’t ready. I quickly became hooked to what is a totally different experience.
The (not always four!) corners on a track aren’t actually identical, but the deal really isn’t learning the track, it’s learning how to survive with 40 other lunatics driving close enough that you can see the whites of their wild eyes. At two hundred miles per hour.
Bad beats are a constant as you’ll frequently be caught up in accidents that weren’t your fault and if you do finish a race you’ll probably have cramp in your hands from white-knuckling the wheel/gamepad.
The game has a career mode and a mode where you start your own team from scratch. I enjoy this series - just don’t tell anyone.