The comments regarding cogging and startup torque would only be true in this case if its a machine which has cores in the coils, or slotted laminates. A single phase machine, same number of coils as magnets, will not cog otherwise, untill current is flowing - so no matter what number of coils you use, startup torque is not an issue if it has not cores in the coils, and/or no slotted laminates. If its the "normal" dual rotor design... startup will always be a none issue no matter how many coils you run with.
If you run with same number of coils per magnet that'd be single phase.
Half the number of coils as magnets would also be single phase.
Single phase seems a bit simpler and there may be a bit more flexibility in how you can wire it up, - that's where the advantages end though.
3 phase will run with much less vibration once current starts to flow. It will make better use of all the conductors both inside, and outside the alternator, and in the end you'll squeeze a bit more power from your machine if you wind it up 3 phase. A simple and effective formula is 3 coils/4 magnets. There are some other interesting winding ideas from windstuffnow that may be more effective for 3 phase output.
Do a search on this board if you want gobs of ideas and opinions and a good way to get even more confused!! ;-)