You could use rubber mounting heads for your fans or just water cool the entire thing. However the cheapest thing to do is get rubber mounting screws. It absorbed the vibration the fan makes against the case.

may be just get better fans , and possibly water cooling 

Try and find a more solid case too opt out that sound I don't have many suggestions as I like the roaring sound of a pc but a good two would be the:

NZXT H440 its a pretty good looking case and according to my pc bro's it is indeed quiet (stylish but costs a bit)

or 

The Be Quiet! Silent Base 800 Case is a lot cheaper than the first and is a bit more effective with being quiet

btw these are both towers so if your a little dud who likes em small look for mid towers n stiff or if you want too go with quieter fans those are pretty easy too find and like Voltage said rubber screws can get rid if that pesky noise :)

Also, trying a big heatsink over your CPU over a stock one or Watercooling may be an option. 

Try and remove as many moving parts as possible.

Fans with the rubber mounting heads as voltage suggested are also your friend!

Linus did a build log video (that was really quiet):

Also check out: http://silentpcreview.com/

get the define r5 or define s and look at buying a couple Venturi or Noctua fans. This works wonders trust me learnt this is the quietest setup not only on the noise level but also the asthetic

try adjusting the speed of your fans in the bios/uefi.

The NZXT s340 is a great case. Quite a bit of space, and can fit a nice cooler in it (not quite a Hyper 212+, but pretty good). The only drawback is it does not have an Optical Drive slot. But the case is super clean, and can add 2 front fans, 1 back, and 2 top fans. Very quiet with some nice Corsiar 120MM Silent fans.

http://www.newegg.com/Product/Product.aspx?Item=N82E16811146197&cm_re=nzxt_s340-_-11-146-197-_-Product

http://www.newegg.com/Product/Product.aspx?Item=N82E16835181021

Go with two fans and a new stock heat sinc its usuly the stock of the CPU

The Corsair SPEC-01 is a great choice. Comes with a built-in 120mm fan and 5 other fan slots.

http://www.amazon.com/Corsair-Carbide-SPEC-01-Gaming-CC-9011050-WW/dp/B00I6BJATW/ref=sr_1_1?ie=UTF8&qid=1448369465&sr=8-1&keywords=corsair+spec-01