This is the best Mario Party game of them all because it has the best mix of strategy and luck out of all the games. It makes a big jump from Mario Party 2 by now allowing you to hold 3 items and not 1.
The addition of a story mode also adds more content to the game that was needed. It sucks that the Mini-Game coaster was removed, but it was replaced by the 1v1 boards which offer its own unique fun.
Overall, if you're looking for the best Mario Party video game to play then Mario Party 3 would be the game for you.