You might want to check out the Completed Builds [Fully Documented] section - the late ARH and Bill Waldorf go into the details of the material they choose for their ships, which are in scales similar to yours. A cursory look at their 1/96 builds suggests frames are 1/8" while the keel is 1/4", and plating at 1/8" or 1/16". That said, ARH's
1/96 North Carolina used 1/2" for the frames, so...
I don't recall them saying why those are chosen, but I suspect it'll be useful for keeping the weight down - easier to transport ballast separately if necessary.
Russ Clark's build of his
1/144 Graf Spee highlights an issue with using 1/4" - they're thick and difficult to cut, and complex curves may result in broken blades.