The rule of thumb is 0.2" of belt and as much bulge as you can fit without losing speed.
A common goal of armor is to "bounce" shells. If you can reach a critical threshold (which varies with the shell, whether we're talking about belt or deck hits, and what angle the shell is coming in at), you can dramatically reduce the shell damage (stopping 90+% of it). That said, effective use of speed and dodging can also result in evading large amounts of enemy firepower. "Speed is armor" applies very strongly to NF.
Several US ships can do with with belt/close in low angle shells in a Blitz (very few shells over 8" and a fair number 6" or smaller), or in rarer cases deck/higher angle shells. Even so, one can use those same ships effectively without armor. In a Great Battle environment, most shells cannot be effectively bounced, and those that can are typically from ships that can be effectively dealt with without using armor.
Against torpedoes, the situation is somewhat different -- every last unit of bulge has an effect in absorbing torpedo damage. Even then, one can use speed and situational awareness to evade a large fraction of torpedoes. (Essentially all of them in a Blitz situation) The 0.2" of belt that Bong suggested is a well tested, light, and surprisingly effective torpedo defense -- damage from hits is roughly halved. (More belt has little effect)
Bulkhead offers the ability to maintain overheat capability (and slow cruise speed loss) with large amounts of damage. The high weight means that you often can't mount much without taking a serious speed hit. If you're able to make torpedoes a non-issue (BB rooms, possibly some blitzes), it can be worth replacing your belt/bulge with a few units of bulk.
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