Hi Dave, I am fairly new and haven't built anything yet.
A lot of sincere and smart people have been working on this for a long time. When it comes time to build, I will stick with a proven design, described by honest people who aren't trying to sell me anything. Do not believe any ads or manufacturer claims.
To get electricity you have to spin magnets next to copper coils. Radial flux means you're spinning a soda can shape inside a slightly larger stationary soda can. Axial flux is like spinning a pancake next to another pancake.
For the one-time expense of adding a second set of spinning magnets on the other side of the stator of coils, the output will be noticeably improved in all conditions.
It is easier to add a second magnet rotor, and then adjust the air-gap to the optimum distance from the stator on an axial flux. On a radial, it is much harder.
Why 3 blades? even numbers of blades have a small problem at high RPM's, so 2 and 4-bladed designs will work, but 3 is better. 5-bladed props are more trouble and expense, but some people have used these in low-wind sites. High blade-count props have more torque, but the high solidity forces some of the wind around the prop instead of through it.
Why 3-phase? One-phase can make a filament bulb noticeably flicker. I think this is called "flutter". Two phase has less flutter, but 3-phase is very smooth for a small additional complexity. 4-phase would work OK, but it would need 4 rectifiers instead of just 3. If you build an odd-phase machine, few people will be able to answer any questions you have.
Voltage? Wind-gens, inverters, and chargers are usually 12, 24, or 48 volts. If you build a 36, 60, or other custom voltage wind-gen, you will also have to build a custom charger and inverter.
"I think" iron-core means steel or iron is put in the center of the copper coils to help focus the magnetic fields. I think air-core just means there is no iron/steel. The coils are usually set in a poured epoxy form that hardens, but they are not called epoxy-cored.
"Mag-Lev" Magnets have two poles, commonly called North and South. Opposite poles attract, and like poles repel each other. If you configured a bunch of magnets so an axle and a frame had like poles that were facing each other, the axle would float in a type of "air bearing". It would have unusually low friction. Strong magnets are expensive, so I don't think it would be worth all the extra trouble.
Above a certain size, there is a cost benefit per output by converting a common industrial electrical motor into a radial PMA by removing the rotor, and altering it to add magnets (if you find a used one at a good price). Here, its called a "Zubbly conversion".
I hope this helps, and I haven't butchered the info too badly.