Modern television classics: Which should be watched first?

I think I've mentioned here before that there was a point some time in the last two years that I kind of stopped caring about the TV shows that I was DVRing. It had nothing to do with the quality of the shows. Nothing changed there, these were still smart and clever programs. Like I said, the change was on my end. I just stopped caring. Episodes backed up on the DVR -- 5, 6, 7 episodes of some shows. I'd go to start watching an episode and I'd make it about 10 minutes before shutting it off. One day, after repeating this pattern, I went through and deleted all but a few episodes of a couple of shows I still watched with some kind of regularity.

Before this big purge, though, my TV dance card was pretty full, and I was pretty happy with the names on my list. It took a lot for a show to make its way onto my schedule, that's why I've never seen an episode of many of the shows that are being considered modern TV classics. No episodes of The Wire. None of The Sopranos or True Detective. No Game of Thrones. None of Breaking Bad, and none of Mad Men. But I feel like I should. These are supposedly great stories well told. It seems like someone who considers himself a storyteller should be familiar with and study what people consider the great stories of the time no matter what medium they're told in. Or am I completely wrong to think that?

So, where do I start? If you had to tell someone who hasn't seen any of these shows where to begin what would you tell them?

P.S. This post isn't out of the blue. It comes from a couple of podcasts I listened to on my way to and from work recently. Chris Hardwick interviewed Vince Gilligan and Matthew Weiner, creators of Breaking Bad and Mad Men respectively, for his Nerdist podcast. The interviews were excellent, but they usually are. Hardwick has a knack for putting subjects at ease and getting them to open up. Not Barbara Walters open up where we get the waterworks, but just get them to talk. I've seen people paid a pretty penny by other organizations to interview people who can't do it as well as he does. If you aren't listening to The Nerdist podcast, you should be.