The "wildchild" phase – an often exciting but harmless time in a young person's life – can take different forms. Some of us decide to try drugs, move into a squat in Seattle, or experiment with new and intriguing coffee blends. And then there's Piper Chapman (Taylor Schilling), the star of Netflix's original new series, Orange is the New Black, who met and fell in love with mysterious older woman and drug smuggler Alex Vause (Laura Prepon), got involved in transporting drug money across international lines and is now having to go to prison, 10 years after the fact. These were all supposed to be just minor adventures, Piper tells her fiance Larry (Jason Biggs), on the way to becoming "the nice blonde lady I was supposed to be".

Series creator Jenji Kohan (who previously made Weeds, another dark comedy-drama with a non-law-abiding lead) mines Chapman's white middle classness for rich comedy; her mother has told friends she is "doing volunteer work in Africa" for the next year. She is the classic entitled and largely clueless "wasp" college graduate – her day job back home in New York is a shared business with her best friend, in which they make boutique soaps and lotions that they're hoping to sell to Barney's. Her one true talent seems to be an uncanny ability to put her foot in it, as she does on her first day when she unwittingly tells prison kitchen head Red (an unrecognisable Kate Mulgrew aka Star Trek's Captain Janeway of the USS Voyager) that the food is disgusting. Her clueless waspiness is a gift for Kohan and her writers – seven episodes in (there are 13, and it's just been commissioned for a second series), Piper has managed to attract friends and make enemies in almost equal measure, and in one case, both in the same person: Crazy Eyes (a standout performance from Uzo Aduba), a would-be lover scorned.

The script is the real star here, though. In the opener, a tearful Piper hugs Larry goodbye with the words, "I love you. Please keep my website updated," after noting earlier that "there'll have been, like, three new generations of iPhones" by the time she gets out. There's a memorable scene in episode three where the idea of phone sex is floated, as brought on by a Whole Foods shopping list of heirloom tomatoes, buffalo mozzarella and organic blueberries. In episode six, the biggest belly laugh comes from support players Poussey (Samira Wiley) and Tasha (Danielle Brooks) doing impressions of white people talking politics: NPR, yoga and wine-tasting all make an appearance. It's sharp social commentary, served on a big bed of comedy. The politics (race, age, class etc) are inescapable. Kohan has said: "You know, you're not gonna go into a network and say, "I want to talk about black women and Latina women and old women in prison." You need a guide. You need a way in. [Piper Kerman, the author of the book the show is based on] was our gateway drug."

It would be impossible to talk about Orange … and not mention the character of Sophia, played by trans actor Laverne Cox. As with the other characters, we learn about Sophia's story via flashback (a device that starts out as grating, but gets better as the show goes on) and at the halfway point, there is not very much beyond her (excellent) casting to suggest that this will be a searing insight or expose into the interior life of trans women. And that's enough. By telling Sophia's story in an uncomplicated, fuss-free way, we get to see a powerful message – trans women are women - and the support and acceptance she (mostly) receives at Litchfield is often not the case in the wider world.

The other members of the supporting cast are no slouches either: Nicky (Natasha Lyonne) is the often the twinkly-eyed source of the best one-liners, Miss Claudette (Michelle Hurst) is a powerhouse of tamped down pain and stoicism, and Morello (Yael Stone) is almost childlike in her actions. All are excellent, if sometimes under-utilised. There are a few men in the cast too, and all are at least a little interesting as well as driving the plots forward. There's prison head Healy (Michael Harney), who seems obsessed with the sex that goes on in the prison, creepy prison counsellor Caputo (Nick Sandow), and correctional officers Bennett, an Afghanistan war veteran (Matt McGorry) and the unremittingly awful Pornstache Mendez (The Wire's Pablo Schreiber), who plumbs new lows of terribleness every episode.

All in all, Orange … is ticking all the right boxes so far – it passes the Bechdel Test with flying colours, it's funny and fresh, with sharp acting and writing. Who knew a show about a privileged white lady going to prison would end up as one of the best new shows of 2013?

• This article was amended on 30 July 2013. We mistakenly referred to Matt McGorry's character, Bennett, as an Iraq war veteran; he was in fact an Afghanistan war veteran. This has now been changed.