GOG is very weak on racing, so if you want serious racing experience, I'm afraid you will have to look elsewhere.
Judging by what you wrote, you're the type for casual arcade racing, so Race Driver GRID is your best car racing choice on GOG. It's very diverse, both tracks and cars, career mode is well done and it will provide you with plenty of fun.
For motorbike racing, Motoracer 1 and 2 still hold well, first has better balance and offers better challenge, while second has editor which allows you to build your own tracks. I even made a track pack long ago and posted it in Motoracer forum, but not sure if any of the uploads still work.
Outside of GOG, I would first recommend you to try RaceRoom Racing Experience, it walks the line between arcade and simulation and it does it very well, and it's partly free (2 circuits, 1 hillclimb, and some cars). Recently they added a lot of diverse content packs at very good prices. The AI has 40 optional difficulties, so you can always find the one matching your skill to keep the challenge up and to take the most of the experience. It feels very satisfying to reach the podium after a challenging one hour race.
It is my personal favorite racing game, I have all available content and I think it is worth it. But I race with racing gear (seat, wheel, pedals, shifter), it may not be that great experience with keyboard or controller. As it's partly free, it's worth trying.
Burnout Paradise: The Ultimate Box is good for relaxing driving through the city and it's surroundings, with optional challenges and multiplayer support. It's pure arcade with wide variety of cars and bikes.
These two I have permanently installed, always returning to them. Also, neither has third-party DRM, just Steam.
Other popular picks are Automobilista, Assetto Corsa (poor AI), Dirt Rally, Project Cars (arcade, very rude devs). Then there's iRacing for serious multiplayer oriented players. What else... rFactor 2.. Trackmanias for building crazy tracks and arcade multiplayer oriented fun. Can't remember what else out of my head.