You can have great heatsinks, a good case and nice smooth fans but you won't get the best from it without good fan speed regulation.
My PC is moderately quiet as it boots but only once it's booted and Speedfan takes control of the fan speeds does it become 'properly' quiet.
The case and CPU fans get slowed to ~25% / 500rpm and the video card has had a BIOS mod to allow the fans to be dropped below 40%, to 25% also.
Some people go for a fixed approach where the fans will cool enough for any load, others like a variable approach where the fans can be speed up as the load increases. This can be with hardware controllers, BIOS control or software. Pros and cons to each method.
These days modern components idle at pretty low power, a moderate gaming PC can now idle ~40-80w for the whole system so even with only reasonably well chosen components you can achieve very quiet at idle PC just by getting the fan speeds under control... As long as the HDD(s) are quiet and soft mounted or better yet SSDs!
As a side note I wish people in general would be more accurate in their use of silent. Silent means something makes no noise at all, not just that it's quiet or drowned out but other noise. It's also an absolute so you can't have degrees of silent or something being 'more silent' than another, it's like saying something is 'more dead!'
PC's can be quiet, very quiet, more quiet, even inaudible but if it has moving parts (or whining electronics) it's NOT SILENT.
How quiet are you aiming for? How quiet is your house/room? Do you want quiet and smooth enough so it 'doesn't bother me' or do you want 'I can't hear it'? And do you want that at full gaming load or is quiet idle and moderate full load ok?
The level of background noise, and hence quietness you might want from a PC will be different in a large city near a busy road compared to a rural location.
It's easy to get hung up on the choice of case but I would suggest choosing one you like the look of and that has the potential to breath well, i.e. large unrestricted fan points. you can then fit the number and speed of fans as per your individual requirements. You can chop out restrictive fan grills and/or block un-needed fan holes if it helps choices. Noise damping is nothing like as effective as slow quiet fans that don't make the noise in the first place.
My PC is in an aluminium case (not recommended for silent builds) that didn't breath well at all. Following significant modification and carefully controlled fans (2x 92mm exhausts on soft mounts ~500rpm) it's so quiet you can't really hear it from sitting position. Not because it's drowned out by background noise, even late at night when I can't really hear anything it's still tough to pick out the noise it makes, in fact the monitor(s) are more distracting!
I guess the point from this is you can make anything quiet with enough work!
In my case: mod the case for airflow, replace 1x80mm exhaust with 2x92mm, swap the PSU fan, fit the largest CPU heatsink that would fit the case and then change the fans on it, fit aftermarket cooler to video card and change the fans on that and mod the video card BIOS, run Speedfan to control CPU and case fan speeds.
Final piece of the puzzle is hard drive(s), for me no PC with a hard mounted hard drive is properly quiet. HDDs are the hardest thing to get really quiet so I recommend SSD as system drive. I would anyway for performance reasons, they make a world of difference like nothing else. For bulk storage I have a WD Green drive in a Scythe Quiet Drive sitting on foam, but network storage would also work depending on your preferences.
For finding stuff on SPCR there is a reference section.
OK some of it is out of date, if you look through a recent case/fan/heatsink review they have comparisons to other comparable recently reviewed items so you can gauge a relative standing from that.
PS don't worry too much about you choices as the way silent PC addiction goes is:
Mod or replace the loudest item, now the next loudest stands out so fix that.
Repeat till you've done everything and the first thing is now the loudest again...
So start over with ever more expensive replacements!