You can't limit it to just 3. You can't even fit all the 'must play' Nintendo consoles in 3 choices.
That said:
1. NES - If you want to play one of the biggest and most influential libraries in the history of gaming, you need to have played the NES.
2. PS2 - Same as NES.
3. 3DS - In theory, you'll be able to play the entire lineup of Game Boy, GBC, GBA and DS on this one system. And you can't ask for a more amazing thing than that.











