Susan Calman's latest show has a delightfully silly title – Calman Before the Storm – which neatly doesn't pin her down to any particular theme but instead allows her to riff on a wide range of subjects. It makes for a pleasing hour of feelgood comedy.

This show started life at the Edinburgh Fringe earlier this year, while the Rio Olympics were taking place; but Calman wasn't worried that she might lose potential audiences. She knows her demographic: “Oh, I’d love to go see Susan, but no… the taekwondo is on!”

Romesh Ranganathan has had an astonishing rise in comedy. The former teacher did his first full-length show at the Edinburgh Fringe in 2013, having made his debut there in 2010 in the newcomer competition, So You Think You're Funny? Now he's a television panel-show regular, and the second series of his travelogue Asian Provocateur is currently on the BBC. His success, he deadpans, is because, with his Sri Lankan heritage and a lazy eye, he ticks not one but two diversity boxes.

You may have thought that the Brexit vote in June would have been manna from heaven for Al Murray as the Pub Landlord, his knucklehead xenophobe creation. But in this uneven and – at two-and-a-half hours – overlong show, the referendum result and what it means for this country is mentioned early on but is hardly the focus of the show.

Five nominations for the Edinburgh Comedy Award are surely a recommendation for James Acaster – and with his intelligent, offbeat humour and a wry delivery, he has rightly built up an impressive following at the Fringe (where I saw this show), having improved his craft year on year. Now he embarks on his biggest tour yet and is certain to add to his rapidly growing fanbase.

Australian stand-up Tom Ballard was nominated for best newcomer in last year's Edinburgh Comedy Awards for Taxis & Rainbows & Hatred; last month he went one better with The World Keeps Happening, which gained him a nomination for the main award.

It's a loose follow-up to the 2015 show – more political observational comedy with a strong social conscience, but with rather less about him being gay. The blokey-looking 26-year-old mentions it early on with a gag about Grindr, but it's a minor element among the political and social comment.

Zoë Coombs Marr, Underbelly Cowgate ★★★

Zoë Coombs Marr's debut show last year, Dave, gained a lot of attention, and rightly so. Dave is an old-school male comic whose line in misogyny doesn't sit well in modern comedy – even if his material might find an audience in the wider world.

Richard Gadd, The Banshee Labyrinth ★★★★★

Richard Gadd wryly tells us at the end of Monkey See Monkey Do that he thought it was a good idea to put this thought-provoking show, with its deep seam of theatricality and emotion, in the comedy section of the Fringe brochure. And in truth it could sit easily as a theatre show, albeit one with frequent laughs. But at its heart is a deeply personal and highly revelatory story about an incident in Gadd's life that caused him to re-evaluate who he is both as a person and as a man.

Bridget Christie, The Stand ★★★★★

When Bridget Christie planned this show, it was to be a work in progress about mortality for a tour starting later this year. But then the EU referendum happened, and everything changed. Within the space of a few weeks, she had written this heartfelt polemic about Brexit, and it's an astonishingly accomplished and moving work.

At least half the audience for this live version of the short-form improv show, which was shown on Channel 4 between 1989 and 1998, couldn’t possibly have seen Whose Line Is It Anyway? when it was first broadcast, so one assumes they must have become fans via YouTube or rerun channels – testimony to the idea that good comedy is timeless and ageless.

David Baddiel's new show, funny though much of it is, raises some interesting ethical questions. Described by the writer and comic as a “massively disrespectful celebration” of his parents' lives, My Family: Not the Sitcom certainly lives up to that, but, considering his mother is dead and his father is suffering from a form of dementia, neither could give their approval for the material used. Yet because it is done with such obvious affection, that becomes a nagging doubt rather than a burning issue during the engrossing 110 minutes.