I'm in the midst of doing some neck turning, and have posted a few questions myself as of recently. As for neck "thickness", I've seen some guys run down as thin as eight-thou, but most have complained about split necks, more frequent annealing being needed, and having to handle the cases more gingerly. <this is on bigger stuff --.30-06 and up> I personally would recommend somewhere around minimum of ten, max of...13. I'm doing a variant of a 6PPC now and have the necks at .01225" more or less on the nose. A lot has to do with the over-all quality of the brass--if it's warped like a hooker's conscious, you may be better off turning it to the minimum side of things, as this may aid alignment.
Please provide info on cartridge and chamber dimension. If you have a reg. SAAMI chamber, neck turning doesn't do a heck of a lot. I would suggest turning just enough to knock off the high spots on 1/3 to 1/2 way around the neck. The thicker necks will keep brass from splitting and with large chamber clearances, the thicker neck may actually improve centering.
Some will even neck down "larger" brass to increase neck thickness before turning. Would not want a neck over 20 thou thick for fear of poor bullet release. 16 thou seems to be norm for a SAAMI chamber.
If you have a tight neck match chamber, then go for 1 to 2 thou of clearance on each side of the neck.
The chamber's neck dimensions will determine the best thickness to use. Neck size if possible and minimize runout during seating. That will improve accuracy more then a few thou of neck thickness difference (SAAMI chamber).
My necks are .0105 and I have 1 thousandth,that is 1/2 per side, to get the case in the chamber with Match Kings. It doesn't get much tighter than that and I feel that the walls are too thin. But from what I am hearing,maybe it is very much on the tight side but still fine.Most of the long range shooters I know don't keep their stuff nearly so tight,or their necks so thin.But really, I haven't talked to that many people. Opinions please.