As someone who has built a gaming build with the intent of keeping it silent, I have to say that the Fractal Design R5 is easily the best case for a silent build. Be quiet makes really good quiet cpu coolers, as their company name would suggest, but you should also check out Scythe. I have the Scythe Mugen 4, and even at load I have trouble hearing it from two feet away, and that's not an exaggeration. You should also consider getting case fans for the Fractal Design R5 that are quieter than the stock fans that come with it. They're quiet, but I feel like there are some aftermarket fans that would do a better job of being quiet. You should also consider psus, as there are fanless psus that specialize in silence, but only so many are quality and a good price. And most important is storage. Hard drives are loud, simple as that. If you want to avoid noise, that's gonna be hard with hard drives, but hard drives are practically a necessity. It's a conundrum for sure. We must also consider the fact that this build is only going ot be used for web browsing. If that is the case you don't exactly need excellent processing power from this thing or anything. It doesn't need to be a graphics powerhouse or anything by any means. So based on this criteria and your budget, the build below is what I'd suggest to you. This build won't make a peep. A very high quality fanless psu with a specifically quiet budget cpu cooler, without any loud HDDs all put inside the Fractal Design R5, which has sound dampening foam on the inside of the case, should prevent you from hearing any noise from this computer. It's within your budget, it still keeps that nice processor you wanted and along with it DDR4 RAM. I can understand if you have some qualms with this build. 500gb isn't a ton of space on a computer, but if you want absolute silence, HDDs are not the way to go. Yeah SSDs are expensive, but they are silent, and 500gb should be enough room for a business computer that mostly just browses the internet. More SSDs can be added later anyways if more storage is needed, or an external storage device could be used. And as for the RAM, I only included 8gb in my build because I don't know what you could possibly be using 16gb of RAM for if you were just web browsing. If the person using this computer has a specific reason for needing 16gb of RAM, like if he uses certain programs that consume a ton of RAM, then he should be fine with just 8gb of RAM, even if he keeps a lot of tabs open in Chrome all day long. This build is within your budget, meets your requirements as far as I am aware, and is ABSOLUTELY silent. So this is my suggestion.
PCPartPicker part list:
http://pcpartpicker.com/p/Ngvs23
Price breakdown by merchant:
http://pcpartpicker.com/p/Ngvs23/by_merchant/
CPU: Intel Core i5-6600K 3.5GHz Quad-Core Processor ($219.99 @ Micro Center)
CPU Cooler: Scythe Mugen 4 79.0 CFM CPU Cooler ($40.50 @ SuperBiiz)
Motherboard: Asus Z170M-PLUS Micro ATX LGA1151 Motherboard ($108.99 @ SuperBiiz)
Memory: Crucial 8GB (2 x 4GB) DDR4-2133 Memory ($45.99 @ Newegg)
Storage: Crucial BX100 500GB 2.5" Solid State Drive ($149.99 @ SuperBiiz)
Video Card: Sapphire Radeon R7 240 2GB Video Card (Purchased For $0.00)
Case: Fractal Design Define R5 Blackout Edition ATX Mid Tower Case ($94.99 @ SuperBiiz)
Power Supply: SeaSonic X Series Fanless 460W 80+ Platinum Certified Fully-Modular Fanless ATX Power Supply ($119.99 @ B&H)
Monitor: AOC I2269VW 60Hz 21.5" Monitor ($99.99 @ Best Buy)
Total: $880.43
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-10-28 22:39 EDT-0400
Edit: If having 1TB of storage is truly a necessity in this scenario, like I said, it's not like you need a whole lot of processing power for web browsing, so if you're okay with it I'd suggest getting the i3 Skylake that is currently available with a cheaper mobo, as it's not like this guy is gonna need a quality mobo for ocing or something. With the extra money you can get a super fast, super quiet 1TB SSD to throw in there. It will run as well as he needs it to, and you better bet that this baby will be silent. Plus with that amount of storage, and the newer Skylake platform and DDR4 RAM, this thing won't need to be upgraded for a while, but he can still continue to upgrade it if he pleases. You'd have to get the Fractal Design R4 instead of the R5, but there are only minor differences between them, and the R4 still has dust filters, so it checks out. How does this look instead?
PCPartPicker part list:
http://pcpartpicker.com/p/HLMX6h
Price breakdown by merchant:
http://pcpartpicker.com/p/HLMX6h/by_merchant/
CPU: Intel Core i3-6100 3.7GHz Dual-Core Processor ($125.99 @ Amazon)
CPU Cooler: Scythe Mugen 4 79.0 CFM CPU Cooler ($40.50 @ SuperBiiz)
Motherboard: ASRock H170M Pro4S Micro ATX LGA1151 Motherboard ($81.00 @ SuperBiiz)
Memory: Crucial 8GB (2 x 4GB) DDR4-2133 Memory ($45.99 @ Newegg)
Storage: Crucial BX100 1TB 2.5" Solid State Drive ($299.99 @ SuperBiiz)
Video Card: Sapphire Radeon R7 240 2GB Video Card (Purchased For $0.00)
Case: Fractal Design Define R4 Blackout ATX Mid Tower Case ($69.99 @ Newegg)
Power Supply: SeaSonic X Series Fanless 460W 80+ Platinum Certified Fully-Modular Fanless ATX Power Supply ($119.99 @ B&H)
Monitor: AOC I2269VW 60Hz 21.5" Monitor ($99.99 @ Best Buy)
Total: $883.44
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-10-28 22:49 EDT-0400