Are there clear ideological differences among the leading candidates? Who would be considered most on the right? Who the wettest? Who the most truly pro Brexit? etc.
Boris Johnson - has tied himself pretty securely to the Brexit mast, although it is well-known among all sides that this was a decision made because of political calculation rather than personal commitment. Has no strong ideological ties in general, although is more prone to state interventionism than the norm.
Dominic Raab - hard libertarian especially irt employment laws and civil liberties; dislikes feminism; pro-Brexit and supported Leave, resigning from his role as Brexit Sec when the WA wasn't to his liking (although he did still vote for the WA)
Steve Baker - most hardline mooted candidate, being an ERG whip and a member of the Cornerstone Group; doctrinaire opponent of EU and supporter of all kinds of oddball right-wing causes like global warming skepticism and returning to the hold standard
Graham Brady - On the right of the party (resigned from Cameron's shadow cabinet because DCam ditched a pledge to reintroduce grammar schools); his role as 1922 Committee Chairman meant he was the "leader" of sorts of the backbench rebellion that ousted May, but also was the author of the only Brexit related deal to achieve a majority in the HoC. Not exactly going to win any awards for charisma. "Sensible Brexiteer", I guess.
Andrea Leadsom - social conservative, prominent Leave campaigner, notable for a pretty lousy 2016 leadership campaign. resigned at the 11th hour of the May premiership, presumably to maintain popularity with the base.
Michael Gove - another Leave person (betraying his close ally David Cameron), although like BoJo one could argue that this was more a tactical decision than one of commitment. One of the few cabinet ministers to stay fairly loyal to May (or at least, he has stayed out the constant undermining and sniping that many ministers seemed to enjoy) despite them loathing each other on a personal level. Has been an unusually "activist" Environmental Secretary, although his previous reign as a controversial Education Sec means he doesn't have a lot of crossover appeal for the left.
Jeremy Hunt - an empty suit who risen through the ranks without much distinction, including surviving scandal as Culture Secretary and an incredibly lethargic period as Heath Secretary. Supported Remain in 2016 and has largely toed the line since, although he was the first cabinet minister to tell May her new WA was dumb.
Rory Stewart - has a very interesting background (look at his Wiki page) and normally regarded as very clever (which can be a curse in disguise for politicians tbh), but his support for Remain and May's deal makes it very hard to imagine him winning.
Amber Rudd - has formed a new faction called the One Nation group (the old Disraeli catchphrase which is often wheeled out when Tory wets feel nostalgic for the pre-Thatcher days) she seems to be making an official stand for the Tory Left (although her fall in the Windfall saga means she is rather tainted for many). [even more ludicrously Justine Greening, a mega wet, has mused about running but that's incredibly unlikely]
Penny Mordaunt - A consistent Brexiteer but not an ideological hardliner. Has an unprivileged background, having to put herself through sixth form while acting as carer for her younger brother and has made a sop to the Tory backbench by protecting Northern Ireland veterans from prosecution. Once made a speech in the Commons about poultry welfare so she could say "cock" loads of times for a bet with her Navy mates. Did not resign during May government.
Liz Truss - another Brexiteer who did not resign during May government. After surviving an odd scandal that threatened to kill her career at birth (she had an affair with Mark Field MP) she became one of the leaders of the libertarian wing of the party, an instinct she carried into government where she often volunteered her own portfolios as potential sources of cuts. Truss has a strong presence on Instagram, and is possibly the only candidate with a page on Know Your Meme.
Esther McVey - hardline Brexiteer who resigned from government in opposition to WA, and possible source of a rebellion to BoJo's right with her new Blue Collar Conservative group. Former TV presenter, so she knows how to work a crowd.
Sajid Javid - once seen as a bit of a hardliner (member of the Cornerstone Group) but decidedly on the middle in the Brexit issue, and hasn't really shone in his Home Secretary brief.