5/64 & 1/16th ring and max bore size
There is no real con to the 1/16 ring stack. It's lighter, less friction, and lasts plenty long. The stock size is 5/64 so most older designs, or stock replacement pistosn still use it. Most everything else uses the thinner rings. End gap is a function of piston and ring manufacturers and use. When in doubt, use the larger recommendation.
On boring any engine... there is no factory max beyond I think .040 depending on year. If this is a race or stroker build, have it sonic tested and see what it can take.