My i3-2120 with HD6850 and HDD is quite as hell in that case. This comes from a stickler for quiet PCs. First 18 months, I couldn't even tell if it was on. And it runs very very cool.
Are aftermarket fans meant for silence? The ones I have are no different/louder than OEM, just provide better cooling for OCing. I had Coolermaster Hyper 212+ in my old PC. It was okay at best. The biggest offender of noise was from GPU, aging HDD & mobo, not CPU fan.
In OP's case, it's not the matter of getting product A vs B. It's about spending more just to get nothing (case & fan). Today's PC's run very quiet and FREE OEM fans perform beautifully.
At idle, they do, but I can't say I have the same experience for under load, with an i5.
P.S.
No Cooler Master fan yet made could be considered even remotely quiet, IMO. Since replacing the fan on a 212+ costs as much as it does for a good one, I previously used to recommend going with a TRUE, TR Macho (or cheaper old-stock HR-01/02), or Scythe Ninja, instead. With Thermalright's available models being spotty, these days, and Scythe NA closing, I know of far fewer really quiet options, without breaking budgets. There are very few affordable heatsinks with provisions for very slow, or no, fans. The little holes in the fins, and wider fin spacing, make a huge difference.
For just the fans, Arctic Cooling, Nexus, Xigmatek, and Bitfenix (I'm pretty sure a couple models are the same as some Scythes) offer fairly quiet fans, though I'm not sure what the best (quietest at lowest settings, while cooling the PC under load) are, w/o undervolting, ATM (any with a sub-1000 RPM minimum, and 4-pin PWM support, aught to be suitable, at least). I got
really used to having Scythe's fans available

. The Nexus YLs are probably the quietest to start, but every sleeve YL I've ever had has gotten noticeably louder, over time. Arctic Cooling's are probably better long-term, but they are costing more, lately, too. There are others, too, but they often get you into the $20+/ea. territory.
The video card is also a problem, but a passive one will sacrifice performance, and push the cooling needs off to the case, while a 3rd-party cooler would be risky (voids warranty, so any screw-up becomes expensive), and add $60-100 to the budget. IME, Asus and Sapphire do a good job of not having fans that whine or buzz at idle, so that's at least an OK compromise. FI, Powercolor is to have a 7850 passive soon, and aside from that, a HD 7750 or GT 640 are the best options, w/o 3rd-party coolers, at least to my knowledge.