BBC Sport is inviting selections: this was mine
I also certainly wouldn't take the gloves off Bairstow, he's kept well this summer and loves keeping, damaging the confidence and morale of one of England's key players would be an incredibly stupid move in my opinion.
My main doubt is number three. Stoneman has shown enough both in his few Test appearances and against our strong bowling attack, but I don't think either Westley or Malan are anywhere near Test standard so I don't see any point in persevering with either. I share the concerns about Hameed in terms of scoring rate and susceptibility to breaking his hands on bouncy pitches, while Root has said he doesn't want to bat 3 and neither Ballance or Hales are suited to batting in the top 3 in red ball cricket. I really don't know who I would go for there... Vince may not be the worst option; he's got a stupid shot in him but at least he looks to have the raw ability to face Test-quality bowling unlike Westley and Malan.
Hales/ Ballance (dependent on form)