Oooh! A topic I have a lot of recent experience with!
Both of my daughters game a lot with me and both started when they were about 2 yrs old. Games we enjoy:
Bit Trip Runner 2
Super Mario Odyssey
Ratchet & Clank
Lovers in a Dangerous Spacetime
Steamworld Dig 2
Lego City Undercover
Various other PC and console games. In general, Bit Trip Runner 2 was great because it’s a 1-button game at the easy levels and gradually increases in difficulty. Whatever you can give them that allows them to learn the controls without getting frustrating is good. Learning to move in a 3D space with twin sticks takes a while, which probably why we have spent 100s of hours with Spelunky.
I’d like to get them into an RPG, like Ni No Kuni, but they do t really have the patience. I think my ~7 yr old is up for Zelda Breath if the Wild soon.
They’re both loving Steamworld Dig 2 and Mario right now.
Also: I do not allow either of them to play iPad at all unless they are on an airplane. I try to make gaming as social as possible for them and found that they get cranky and argue when they play with iPads.
Edit: I should amend that slightly. I have an iPad Pro with an Apple Pencil and they’re allowed to draw on it, but usually only when they are sitting together and taking turns. The Toca Boca games, which they play sometimes on the airplane, are really good, wholesome, ad-free experiences.