A lot of people would consider Twin Peaks as "the start of modern television" because it was very unique and artsy for television at the time, both Lynch and Frost had a lot of freedom regarding the show and while it has its ups and downs, it was definitely a genuine "film quality on TV" style experience uncommon in the 90s. On the other hand, while Twin Peaks was a laboratory for Frost, Lynch really didn't care about TV, he just wanted to do his stuff and not having to deal with producers, that's why as soon as they tried to twist his arm he left the show and that's mostly why season 2 feels disjointed and out of touch. Season 1 was "okay guys do your magic and let's see how it turns" and season 2 was a producers struggle.
What I would consider "debut of modern television" is definitely Oz in 1997. With Oz, Tom Fontana (which did Homicide : Life on the street at NBC, a cop drama where David Simon wrote) basically had carte blanche as a writer / creator and was probably the first "showrunner" as we know today, where directors / producers were at the backseat of creation. in 1997 Oz was utterly trangressive, dealt with a lot of stuff not seen on TV, had multiple story arcs on many episodes and had top notch acting and writing. Fontana had so much freedom he could write about prison brutality, rape, gangs, murder, suicide, loneliness etc no TV show would even touch in 1997.
Also let's not forget Oz paved the way for "HBO TV golden era" with The Sopranos and The Wire. During the early 2000, you'd also have The Shield of course, also Six Feet Under, 24 and a lot of other top notch TV shows, but The Sopranos / The Wire was at the time and maybe now the best product quality wise you can make with the "showrunner runs all" model Fontana pioneered with Oz (and it's funny to look back how at the time The Sopranos was heavily praised and got a lot of rewards while The Wire was mostly frowned upon). I'm not gonna say everything was about HBO before, AMC kind of replied to HBO years after with heavy hitters like Breaking Bad, Mad Men, Rubicon, etc. Also other networks did L O S T, Battlestar Galactica, Firefly and the list goes on. HBO didn't sleep on its laurels either, they did both Rome, Deadwood or Boardwalk Empire.
Enough derail though, I think The Shield was a precursor in 2002 as a "cop drama where villains wear a badge". Of course you'd see crooked cops in any TV show around, but The Shield pilot was so shocking and engaging at the time, even for a "cop drama", that the viewer had to really think about the actions Mackey and his buddies did, rather than most "okay let me guess who's the perp" cop dramas at the time. I really despise Kurt Sutter taking the showrunner lead (Shawn Ryan left to create The Unit, what a waste) but The Shield has right now one of the most satisfying, concluding ending I could think of.
At the end it really shows how corrupt and wrong Mackey is as a human. He used his family, his job and his friends as reasons to do wrong for being right, but at the end he's just a plain villain, a self-centered, tourmented psychopathic figure with no redeeming qualities at all. He was the anti Jack Bauer, also a controversial main protagonist of another TV show during the time. What a ride the 2000 were TV wise, you could be in any random month at the time and watch The Wire, The Sopranos, 24, The Shield during the same week. Heh.