I think 12mm is correct bar spacing.
As for cage size larger is in most cases better.
With any of the birds I have upgraded to a larger cage I have found they seem to be happy with. And in some cases walk in before I have even had to push them in that direction.
Coickatiel Cottage should have the details you are looking for, plus a lot of other great info.
AS long as your bird cannot put his head between the bars any kind of cage is good....good luck
I want to get my tiel a new cage but I know they always say no such thing as a cage too big but obviously when it comes to the bar spacing getting a cage made for a larger parrot can be a problem I want a cage that usually is made for larger parrots because I want him to have as much room for his large wing span as possible. since cockatiels are quite small birds but with a long tail and a large wing span it makes buying a cage difficult most of the cages with the right bar spacing tend to be a little small, not totally uncomfortable but just not as big as I would like and I can't remember what the bar spacing max is please help?