Stoke City were founded 1863 and they alongside Notts County were part of 12 founding members of a professional League System in England. I think that the first club registered was Sheffield F.C. although not a professional club. Notts County were the first professional club with Stoke formed in 1860, being the second to be a registered professional club when they registered as such in 1863.
The original first professional club league comprised...
Accrington, Aston Villa, Blackburn, Bolton, Burnley, Derby, Everton, Notts. County, Preston North End, Stoke, West Bromwich Albion, Wolverhampton Wanderers.