So, now that I have my budget gaming PC up and running and kids would like to have a wheel and pedals to play racing games. Which games would be good options (preferreably from Steam)?

It's a plus if the game has a Lamborghini Gallardo, as it currently is the favourite car of my younger daughter (13 in a few months) and the most beautiful car in the world according to her (although I argued it's Volvo V70 P2) and she'd want to drive one in a game. 

Basically my favourite racing games/driving sims have been Colin McRae Rally 2.0 and Gran Turismo, so it would be preferred to find similar type of game(s). There are quite many on Steam, but I don't know which ones are worth buying and which are not. 

Most immediate ones that come to mind would be Assetto Corso and BeamNG.drive that’s been running for 10 years and constantly updated. Then there’s Tokyo Extreme Racer that just made its triumphant return!

Then there’s the like of Forza Horizon 5 for pure arcade racing.

I'll assume you have a wheel for these two. Assetto Corsa and Project CARS, two sims like GT7 but more hard core and you can tailor Pro CARs to your liking and make it easy like GT7.

If you don't have a wheel and wanna play solo, DiRT4 trumped DiRT Rally as my favourite Rally game and it's way better than DiRT Rally 2 which fell short for me of the first. 

If you wanna play online with both wheel or controller, DriftX racing online is a ridiculous amount of fun and easily the best drift racer out there, a ton of fun but you make that fun yourself, don't expect a robust campaign.I play Solo but I can only imagine how fun it would be with a group of friends.

Was gonna make a bad suggestion. Ignore. 

My two favorite racing games are FlatOut 2 (2006) and Dirt 2 (2009).