I am sure you will find someone that will give you things set in stone, but in reality I don't think that is the case.
There is some logic in making the gap about twice the magnet thickness so that you are close to the BH max point of the magnets, but then you have to have safe mechanical gaps on either side of the stator and these are much the same for thick magnets as thin ones. The wider the gap the lower the flux density in the gap, but the more winding space you have, so over a fair range things more or less balance out.
For 1/4" magnets I would not try to make the coils much over 5/16" thick as with two safe mechanical gaps you are already looking at a total air gap of 1/2" or more. Same for the 1/2" magnets i would tend to not let the total gap get much over 1" so that means coils nearer 3/4".
It doesn't really matter that much as long as you choose the coil turns and wire size to suit the gap, many people end up having to widen the gap when they find things stalling so if you started with a 1" total gap you may end up with something a fair bit wider.
As long as you do a test coil then the gap doesn't matter a great deal, but if you want to dive in without test coils then you can probably assume you will have a gap flux of 700mT with a 1" gap with the 1/2" magnets or 1/2" gap with 1/4" magnets.
Thin stators use less turns, but you have less winding space. Thick stators need more turns but there is more room. I suspect the cooling is better with thinner stators as the majority of the turns are nearer the surface but I don't know of any tests to prove this.
