Litz wire can offer some advantages. It is not necessary however. Mind you, if you are doing multifilars it can make things alot easier when winding.
Solidstate is good. You can build the Bedini circuit slightly different and it will self oscillate. Or you can just jack up resistance on the base of the transistor. Usually in the 2k plus range and it will self oscillate.
You will get higher rate of oscillations with air cores, or you could wind an iron wire within your multifilars. I have yet to try this, but it has been suggested by John himself as one way you can lower the oscillation speed. The iron or steel wire must not retain magnetism and should be insulated.
You can also try a single recovery winding which goes to bridge rectifier, and then straight to charging battery. In this config you have your SG circuit with "x" amount of power windings and a separate length which is your recovery winding. It is inductively coupled and will pick up your spikes for you, while not being directly connected to the power windings. In this case you dont need diodes off the collector/s. And dont use a neon. Just make sure your battery is ALWAYS connected. Either that or put a cap on the bridge. Which leads you to learn and discover the capacitive discharge configuration...... so many circuits to learn and build.
