I've set up tanks without any cloudiness using flourite.
I put the substrate in, no water, and then I plant, and while I'm planting I'll periodically spray the whole tank down with treated water in a misting bottle. I'll do this fairly heavily a few times while planting, and then again after I'm done planting. Then I'll stick a spare filter sponge or something in, and slowly pour the water onto that.
I think the spraying helps wash the fines down lower into the substrate, and the sponge helps break up/diffuse the water flow so it doesn't disturb the substrate.
Another method I've seen people post vids of (I've used it myself once) is to take a soda/water bottle, put your substrate in that, fill it with water, put it in the tank, invert it, and let the substrate fall out. pretty much all of the cloudiness remains in the bottle, which you then turn right side up, take out, and dump in a planter/sink/whatever, and repeat.
For clearing the water, carbon won't do much - that only really helps with organics like tannins. floss might be the cheapest, but keep an eye on it and change it fairly frequently so it doesn't slow your flowrate too much.