Another vote for Leapster. We dont have the LMax though, and probably wouldnt use it. The Leapster goes in the car, and is handy when sitting through dinners, and visits with grandma. My son got it when he was 3 and has learned a lot from it (hes now 5). The games grow with the child. It is durable and has survived many drops.
The other month, the touch screen gave out after a hard drop. I called Leap Frog and since they have upgraded their system, the rechargable battery pack on the old system no longer works on the new one. Also since we already owned one, they gave me a 50% off deal. I ended up getting a new Leapster and a new rechargable system for half price. Bottom line-their customer service is good!
As soon as dd (2) is old enough she will be getting her own Leapster. She is already trying to play with her brother's. The good news there is that we can recycle the preschool games!