I really don't care which case you use, and I can't tell where in the case you're going to put that core, so get your tape measure out, and let me know!
Keep in mind that you'll want to shroud that, so on top of the 1 in thick fan, add another inch for space between the core and fan (shroud), and figure about 2 inches for the core itself.
I disagree with Heavy_Equipment. If your goal is to eliminate the fans, then watercooling the GPU is not unreasonable. If your confidence level is low though, then you might consider the GPU WB as an add-on, for later.
Go ahead and use 3/8 for the GPU block, and 1/2 otherwise. If you want to stick to 3/8, that's up to you: it's reasonable for the purpose of making a system quiet (1/2 would be better for an overclock).