Home-made Giant batteries
There are so many technical difficulties to overcome, in catching lightning, it will probably never be used to generate electricity.
However, if you want to catch the energy of lightning, the wire wouldn't need to be bigger than that used for lightning strike protection in buildings (about 8mm accross) or smaller.
You can use capacitors or coils to store energy, like a battery, but not much energy. My watch has a capacitor instead of a battery (it is a Seiko Kenetic) - it only stores enough energy to run the watch for a few days if I take it off.
As you suggested a better way of storing energy might be steam. If you direct your lightning bolt down your wire and get it to jump a gap, it will give off a lot of heat which can be used to turn water into steam which can drive a generator.