Kids games take a lot out of a computer. Kids games is what forced me to upgrade ALL my Macs from 68000 processors to PowerPC, then forced me again later to move to Intel Macs.
The "entry-level" Mac is the Mac Mini, which I think of as a low-end portable-class machine without a display. An older MacBook (maybe a used one with a lousy battery) is also an option for kids.
Your kid will be 3 years old for a very short time, then will have increasingly demanding computer needs. The life-cycle of each game is also remarkably short, as their development level changes very rapidly and the games cannot remain interesting for very long.
You cannot win. The moment you think you have the problem solved, they will master the game, become bored with it, and abandon it. That is a good thing, because it indicates they have progress, but this becomes a never-ending battle to find worthwhile, engaging edu-tainment software.
There are two basic classes of software -- pre-reading and reading. In the latter category, "ClueFinders" titles have proved very worthwhile in our house, but I am no longer sure what systems they run on, as they were 68000 and PowerPC programs when issued.