Stock cooler might work. Try it out and see if you're happy with it. Boot with just the psu, cpu, ram and one ssd connected to the mobo (to keep other noises to a minimum), and see what the noise is like (use the computer like you would in real life, playing videos, some basic games...). If it's already too loud, replace the cpu cooler (if I were you, I'd get a nice tower cooler and run it passive = no noise)
As for mini itx, why not. It's more of an expansion slot question really... Will you ever need the extra slots ?
As for the case, there are endless options... you could make one
Or you can pick the box you like first, and then see what fits in it. It can be tricky because some mini itx cases have clearance issues for cpu coolers, video card length, psu size, fan size.... If a box is just a container, pick the quietest components first, and then the case.
Did you check out the sample builds that SPCR put out some time ago ? It can give you an idea as to what fits in what case with noise measurements.