This is a tough question to answer with only one game. But I think I’ll go with the one we started playing when our weekly gaming group first started, Risk Legacy. Risk Legacy takes an old game people have probably at some point played and adds the greatest thing ever, a customizable game board and card deck. A 15 game campaign leads you through the evolution of the land using stickers and writing on the board. You have the option to keep playing with the same faction and adding to their powers.
The box is pretty awesome and upon opening it you’ll see a series of sealed envelopes that contain cards as well as sealed compartments in the box that can totally change the game. These things can only be opened when specific thing have taken place in the game such as when a player gets eliminated for the first time. It’s a little hard to not spoil the surprises that come along the way.
Why this makes a good introductory? It gives new players something they’re somewhat familiar with while keeping it interesting and different. It takes strategy but the constantly changing game play (which is very well laid out in the rule book for easy rule referencing) makes it so everyone has a fair chance to win. Also, whoever wins the 15 game campaign can keep the game board for a trophy. If only it wasn’t spoilery to tell you what is in those sealed envelopes and compartments.