I've now got well into rigging my Camel fighter, and as with anything new it's learning on the job (with a steep learning curve), so have been trying different techniques and settling on what I find works the best for me, and making reasonable progress (better than expected).
For thread types, I've learned before never to use cotton or similar textile threads as they have fibres protruding along their length, so have purchased a reel of nylon invisible mending thread as mentioned above, and a reel of reasonably fine black nylon thread (available at Hobbycraft or Dunelm Mills (in the UK)). The invisible thread is so fine I thought I'd keep it for antenna wires on WWII aircraft and decided to use the slightly thicker but still very fine black nylon thread.
Applying to the aircraft is a whole science in itself !!! I thought I'd build up the fuselage and lower wing with struts and leave the top wing off, to gain easy access to add the wing bracing wires, so added a few strands from the lower wing to the top of the struts quite successfully, then tried the top wing for size and as they were very slightly out of alignment, the bracing wires lost a bit of their tension and sagged slightly, so it was back to the drawing board. I soon decided that I had no option but to fully build it up including the top wing to form the complete main structure, and start again with the rigging.
I found the best method to attach the rigging at the wing points (base of the struts) was to put a small drop of glue using the Humbrol fine applicator at the attachment points and a tiny drop at the end of the thread, touched the two together and pushed into place with a needle pointed tool, cut the other end off the reel with excess length, and left to set, then repeated for other bits of the rigging while the first end dried. After leaving it for a bit I went back to the first piece attached at one end and pulled the other end of the thread taught and snipped off the excess so it was exactly the correct length, and placed a tiny drop of glue again at the end of the thread and at the upper base of the strut, and pulled the thread up into position with tweezers, then pulled tight in using the needle ended tool, and held for about 30 seconds while it set (occasional rotating the needle tool so it didn't bond to anything), then removed the needle tool away and the rigging piece was left nice and taught.
The good thing about this method is it is fairly quick and a lot of rigging pieces can be done a in a fairly short time (around a two hour session)
In other positions such as the tail and undercarriage bracing, it was easy to drill tiny holes by hand with a micro drill, thread through and apply tiny drop of glue at each point.
It's nearing completion of the rigging now (thankfully much more rapidly than expected), so will try to get some photos posted soon.
Others of you may do it completely different to the method I've evolved as described above, but I thought I'd just share my findings having tried it for myself.