Leek's lovely, a really 'up and coming' town - lots of lovely indy shops moving in to fill the holes left by chains leaving, annual blues festival, relatively lively arts centre, food and crafts markets, nice pubs and cafes, and right on the doorstep of the Peak District.
Being in Staffs rather than Cheshire, £800k will buy you most places on the market! Bear in mind that most of the housing stock that is a walk away from the town centre is smaller/cheaper/less outdoor space than you probably expect given your budget. Lovely bigger period houses out in the surrounding countryside, but you'd need the car more. I wouldn't worry too much about winter - as a PP said, maybe a day or two every other year that you might not be able to get into Stoke. Be warned if you have teens - not loads for them to do, so they will probably spend a fair bit of time taking buses 'up Hanley'.
Buxton - longer to get to Stoke, with more issues in winter. Stunning surrounding countryside. The town has beautiful architecture, but the shops, cafes, pubs etc I find a lot more down at heel than in Leek (I was suprised, was expecting Buxton to be quite chi-chi). Many more big and beautiful houses near the centre though, as it was THE place to be in Victorian times.
Stone - not been there much, but it's got a train link to Stoke, and people who live there seem to love it. House prices a but more expensive. As a town, I prefer Leek, and the surrounding countryside is far nicer in Leek.
@Emarosa feel free to PM me if you have any questions about Leek.