A thing to remember is that VAWTs (except for the likes of the Darrieus) run at a much lower TSR than HAWTs. Savonius designs run under load at something like 0.8, while a typical HAWT runs at something in the range of 6 or so. (Not sure where the Lenz ends up but I'd bet it's close to the Savonius.)
This will impact your alternator design.
If you get your cross section by going with a tall, narrow design you might end up with about the same RPM as a HAWT and be able to use the same alternator designs. If you're closer to a square cross-section you'll have to accept the lower RPM and design for it.
That means a larger radius for the alternator, and perhaps more magnets and copper, to get adequate performance without a speed-increasing transmission.
Fortunately, with a VAWT an axial-flux genny is edge-on to the wind and isn't an obstruction to it. So it can be made with a radius up to the width of the swept area without affecting the mill's wind performance or footprint.