Danny Bhoy is big in Scotland and Canada and huge Down Under, as they say, but is a surprisingly unfamiliar name to many. I'm not sure, other than a lack of a television presence, why he's not as well-known throughout the UK as he should be: he's an extremely affable, laidback Scot whose brand of observational, conversational comedy is easy on the ear.

Kevin Bridges, an affable young Glaswegian, has had a meteoric rise in comedy. He started gigging at 17, made his solo Edinburgh Fringe debut in 2009, where he played in a 50-seater and earned an Edinburgh Comedy Awards newcomer nomination, and returned the following year to a sold-out run in a 700-seat theatre.

First a confession: I've never been a great fan of Michael McIntyre. He's a nice bloke for sure, works at his craft and is a slick performer with a huge following, both live and on television. Plus - and this is one of the best compliments I can pay to a stand-up because it's a difficult skill to pull off - he's one of the best MCs in the business. But I can't get past the feeling that some of his material, to borrow shamelessly from another context, has the whiff of previously used about it.

John Cage is funny: this much we know. The deadpan prankster at the heart of 20^th-century artistic experimentalism was always about the inadvertent punchline, the chuckle that comes from unexpected disjunction, the relief that comes from reminders of the absurdity of reality, as much as he was ever about any engagement with progress, technology, the transcendent. It's entirely natural, then, that Stewart Lee (pictured below), who has spent his whole career reaching outwards from the comedy circuit towards the avant-garde, should want to present his work.

James Acaster: Prompt, Pleasance Courtyard ***

James Acaster has certainly been studying his craft since he made his Fringe debut with an unmemorable show last year, and it shows in Prompt. Lots of comedy tropes are utilised, some of them to great effect, while others feel simply mechanical. He uses repetition, callbacks, audience participation in a show full of whimsy and the most surprising subjects for comedy.

Tony Law: Maximum Noonsense, The Stand 

Tony Law, Canadian by way of Trinidad and Tobago, has been kicking around the comedy circuit for several years with a style of madcap humour that many have delighted in but others have found self-indulgent. But with Maximum Noonsense he has retained all the free-flowing joy of his comedy while reining in some of the slacker elements. It's a marvellous concoction of silliness and sly humour.

Alfie Moore: I Predicted a Riot, Pleasance Courtyard ****

I, Tommy, Gilded Balloon ****

Everybody will be familiar with Tommy Sheridan's story, and not necessarily because they closely follow Scottish politics at their most internecine. Rather because the Glaswegian socialist went from being barely a paragraph in broadsheets to being plastered over the front pages of tabloids after a series of revelations – which he strongly denies – about visiting swingers' clubs.

Tam o' Shanter, Assembly Hall ****

Scottish schoolchildren are brought up on Robert Burns but other British students aren't so fortunate. We may know snatches of the great man's work – “Wee, sleekit, cow'rin, tim'rous beastie”, “O, my Luve's like a red, red rose” and so on – but few of us could recite even a stanza of Tam o' Shanter.

Jigsy, Assembly Rooms ****

Les Dennis may have started his career as a comic, and then as a presenter of cheesy, family-friendly television game shows, but of late he has been plying his trade as a very decent actor. And so it proves again in Tony Staveacre's one-man play about a washed up Liverpudlian club comic.