Hi Other David,
I think how you hook up the coils is a question of how flexible you want the generator to be in the future if you decide to change the configuration of the wiring. I've many times had the two leads from each coil exit the stator and then configured the coils in series or parallel depending on the voltage I was trying to achieve. I think the only real planning you need to do is pick a number of coils that suits the possibilities that you may entertain in the future.
So for example, if you are doing a single phase machine and you have 6 coils, you can wire them 6 in series, 2x3, 3x2 or all in parallel. The single phase will have the most noticeable pulsing since your output will be one giant sine wave. I've done this series/parallel thing on both a single phase 6 coil machine and a 12 coil 3 phase machine.
There are two kinds of pulsing and cogging that can occur. One is from the rising and dropping load that the alternator is generating, which generally isn't too much of an issue with an axial flux alternator (highly suggest you make one of these). The other kind of cogging is when a magnet gets near a piece of iron. This is generally only an issue if you decide to try and have iron or laminations in your alternator... a good example of this would be any brushless hobby motor for a rc car or plane or a servo motor for a machine. This cogging can be quite high and be challenging to overcome with just the torque of your blades.
I wouldn't recommend adding a single phase rectifier to every coil since you will loose 0.7-1 volts, which can add up to a significant amount for just about any reasonably size alternator for a windmill. You might be able to get away with it on a very high turn coil with thin wire, but you would be much better off wiring it up in the typical 3 phase star pattern. 3 phase bridge rectifiers are fairly cheap to buy compared to the wire and magnets.