When I worked retail, I would always direct people to things like a leap pad or VTech thingy until about 5-6 years old.
There are some games where you can set it up that they can just press buttons and neat things will happen and they won't die or anything (Mario Kart with auto steering on maybe) but they won't really be doing anything intellectually engaging. They're not doing anything intentional, just mashing buttons while shit happens.
With games specifically designed for kids, there is a clear cause and effect to what they're doing, and actual intention behind their actions. So, they're intrinsically more educational, plus the content will likely be geared towards what they'll start learning in preschool which is an added bonus.
If you really insist on letting them play on a console, then I'd say Wii Sports is the best starting point. In Tennis, there is a clear connection between what they're doing and what's happening on the screen, and there are no buttons just swing when the ball is in the right spot. If they get that, you can move on to baseball where they can, but don't have to, use buttons, and so on. Wii Sports is basically a tutorial to go from newbie to somewhat competent gamer, so it's the best starting point.