Maybe have a look at the Cooler Master Elite 335 Black ATX Mid Tower Case
. It's currently out of stock at NCIX but it looks like a possible good place to start.
You will have to do some modding to get it quiet though. (E.g. cut out front and rear fan grills, cover up other intake holes in left side panel, apply mass damping materials to stop vibrations from thin case etc.)
This is going to be true for most cheap cases, as cheap and quiet generally don't apply at the price range you seem to be looking at - approx $60CDN for a case without a power supply, based on your looking at the Antec 300 / $150CDN with included PSU, based on the Sonata III (500) you mentioned.
You might want to look at the Antec NSK6580B Super Mid Tower Case with included PSU
Take out the removable HDD cage, suspend your HDD in front of the front fan area instead, get a quiet 120mm for rear exhaust and you may not need front intake fans at all if your system isn't going to be too beefy and will rely on integrated graphics only.
Or, since your first post says you've bought a micro ATX motherboard already, perhaps you might want to look at the Antec NSK3480 with included PSU
Again, if you swapped the rear included fan for a better quiet fan, you could probably get away with just the rear fan.
To answer your original question about sources of noise, case fans, HDDs, CPU and GPU coolers and PSU fans can all contribute to noise. Usually the included fans that come with cases aren't too great and should be replaced with the quiet fan brands that thejamppa mentioned.
The PSUs that come with some Antec cases are reasonably quiet but not the quiestest PSUs on the market today. However, if you are budget constrained a PSU and case combo from Antec can be pretty good value. (See suggestions above.)
You should be considering an aftermarket CPU cooler, as the stock ones that come with CPUs are not always quiet. the Scythe Mugen 2
is only $10CDN more than the Alpine 64 PWM that thejamppa mentioned, so this might be a good choice if your budget can stretch that far.
You're already planning on suspending your HDD, so that will be good.
Hopefully there's something of help to you in all the rambling above...