As the Labour party gears up for another leadership election, the field comes into focus: Jess Phillips, Lisa Nandy and Rebecca Long-Bailey are certain to run. Richard Burgon has both said he will and he won’t; Keir Starmer hasn’t and will. Emily Thornberry was always hotly tipped, though may have been torpedoed when Caroline Flint allegedly accused her of calling “red wall” voters stupid. Yvette Cooper is still in the mix, as are Angela Rayner, Clive Lewis and David Lammy. They criss-cross all the obvious faultlines – Blairite versus Corbynite, authentic Labour versus metropolitan elite, Len McCluskey stooge versus independent mind and, of course, leaver versus remainer. Beyond those caricatures, however, are some genuinely interesting questions about the party’s future.

Phillips is the right’s candidate. This may seem unfair, as on some issues, such as migration, she has taken a far more progressive position than would be considered typical of the right of the party. Indeed, she has surpassed much of the left on this. But her positioning is centre-right. She has charisma; if any centrist candidate could muster their own entryists (centryists, we’re calling them), it would be her. Indeed, that’s her only obvious path to victory – a mass join-up of Jess Phillips superfans – since it’s hard to imagine existing Labour members swinging to such a different candidate.

Lisa Nandy was deeply opposed to a second referendum, wedded to the line that the first one was the ultimate act of democracy, and had to be protected from those trying to stop it. However, unlike almost anyone else of that view, she is personally popular with remainers as well as leavers. Calling her the Blue Labour candidate would be an oversimplification, but there’s certainly an element of that ideology to her worldview, which appears to be that the white working class of the left-behind north are fundamentally different to their peers in the cities, and only when the Labour party understands and prioritises them will it rediscover its soul. Her problem will be what happens when she’s head-to-head with Rebecca Long-Bailey, if Unite still backs the latter.

But will it? Long-Bailey is currently the favourite, the choice of both McCluskey and John McDonnell. Until six months ago it was taken as read that the members would naturally fall in with whomever the inner circle anointed. So, it seemed, there would be a coin-toss between Long-Bailey and Angela Rayner, who were both put at the centre of the election campaign. But what a poisoned chalice that was: they are both now tainted with having to make the case for Labour’s weak Brexit position, neither fully leave nor fully remain, and both undermined by that squirrelly equivocation that is the hallmark of the loyalist (the same holds for Burgon).

The bitter rows over what was wrong with Labour’s Brexit position are easily resolved by the data: it lost nearly twice as many votes to pro-remain parties as it did to the Conservatives and Brexit party combined. But even had the deserters been mainly leavers, that would have been no vindication for those who were sent out with a neither-fish-nor-fowl offer that nobody wanted to eat. That doesn’t mean that Long-Bailey and Rayner are without promise, but they could both use some clear blue water between themselves and Corbyn if they’re to be judged on their own merits. There are rumours that Rayner is considering going for deputy instead, perhaps mindful of this. Nobody will have Corbyn’s 2015 boon of being the only leftwing candidate on the ballot.

It is very difficult to see how Yvette Cooper could present herself as anything other than a return to the pre-Corbyn era – as disappointed as they are, there’s no sign party members are wishing for that. Thornberry has better differentiation from the old days, but was more compromised by her time in the shadow cabinet, especially in the runup to the election, when the party Rees-Mogged her.

Keir Starmer has been the face of remain, but given the views of the members, that isn’t the problem that Lexiters think it is: rather, he faces the irrefutable charge of not being female. Some of this is plainly disingenuous. The Corbyn circle had no problem at all employing a lot of white men, plus their children and/or ex-girlfriends, yet is happy to point the finger at other factions. While “it has to be a woman” isn’t a universal view across the party, there’s certainly a sense that you need a very good reason not to be one. Starmer’s other task will be to persuade members that he’s not a technocratic, centrist, north London lawyer; rather, he’s a political radical who has seen the merit in the Corbyn project and wants to extend it beyond the man. Clive Lewis is seen as leftier, and has great green credentials, but he’s quite a maverick and may yet decide that there are other positions in which he could be more radical and adventurous.

David Lammy is popular in his own right, and an increasingly impressive orator, with years of parliamentary experience. Plus, there’s this blindspot about race in the debate: Labour’s ethnic-minority vote was rock solid, but there have already been calls for the party to focus its efforts on the “white working class”. A good way to corrode the soul of a party – perhaps the best way – is to bank the people who actually support you and chase everyone else. Lammy doesn’t bank these voters. And now we have a card-carrying bigot in Downing Street, a strong anti-racist opposition leader will be vital. Even if he doesn’t stand, who he endorses will matter.

There’s an important question about whom the Conservatives will fear most, and whom they’d be right to fear, but far more vital is that Labour members – and spectators, for that matter – actually listen to the candidates before they commit. Part of the left’s singular problem with division is the tendency to try to talk to one another through carrier issues – if not Brexit then migration, or to which circle of hell Tony Blair and Chris Williamson belong – and identify who we’re talking to, whether they’re of our tribe, without actually hearing them.

• Zoe Williams is a Guardian columnist