What Games to Play?

I enjoy a lot of different games these days, and though I may not be so into board games as some people in the board game world are, I still know a few things about them (from a fun perspective)[1]. Chess (960 especially) and Go and Shogi are my favs, but I have enjoyed the more imaginative ones as well as ones that include luck (always a huge part of life). This goes with poker as well as others like Settlers of Catan etc. Now, there are ones like Fog of War (only playable on a computer) which are a joy to play (and include luck). Dixit is a more imaginative one and... well that's it. 
See, the thing is, I'm thinking of what games should be played together and with the younger generation of our entire family. I do know that I have to be more patient than when I tried to teach chess to my cousin, back in the day. 
Your thoughts?
[1] This means games with complex mechanisms, like Twilight Struggle, get low marks from me, especially since we are talking about a rule set that takes too long to learn. I suppose, I'm partial to the oldies, like go or chess, which have few rules to learn and build out complexity on that. Maybe lawyers or others will feel differently, and maybe the world really is just complex and baroque rules that we have to learn and this speaks to my biases and weaknesses as a human. 

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