I have never seen inside those fans so I cant really advise what size of wire to use. Have you watched the Imhotep rewind video I linked to before? to wind bifilar you use two wires, trifilar, three and so on. Get however many spools of wire that you want and take the end of the wire from each spool, all at the same time and wind like in the video.
Remember it is the amps x the number of turns that make the motor run, not the volts, so you want low resistance coils. the trigger, if it is the same size as the power coils will be in resonance so more of the power will be passed to it via the transformer effect. Ideally we want the power in the trigger coil to match the Beta ratio of the transistor. So if you have a 10 to 1 transistor you only need a tenth of the current or voltage (I forget which it is) on the trigger. Having the trigger wire smaller than the power wires with the same number of turns, takes it out of resonance so the transformer effect will be less. This is what we want because we want all the power going to the batteries.
If you use a bifilar coil you have a 1 to 1 transfer of current to the trigger. If you have a trifilar coil you have a 2 to one transfer or only half as much in the trigger. This means that a trifilar will be more efficient than the bifilar. If you are using a 7 filar, this will be about as efficient as you can get provided that the trigger wire is in the center of the other six wires. Once you get to trifilar and above there is less need to take the trigger coil out of resonance so less need for the smaller wire.
It is difficult to keep the trigger wire in the center of the other six unless you twist the strands. When it is twisted it is known as litz wire.
This site is a great resource on the Bedini stuff and he has Bedini's original drawings posted http://www.fight-4-truth.com/Schematics.html
This picture shows a close up of a damaged coil made up with the litz wire http://www.fight-4-truth.com/Cr.%20Site%20ab.jpg
Stop thinking about volts, you want this to run on as low a voltage as possible, ideally just lower than the charging voltage. The inductance of the coils will give you the voltage on the output to make the battery charge. Ideally you want the current draw of the fan to be 1/20th of the Ah rating of the charging battery. Forget what it says on the fan, it will be different when you have wired it as a SG or SSG
This might be a little advanced if you are just starting, but if you have any questions I will do my best to answer.
Hope this helps