This is a work in progress. I'm building the PC now, so my comments are more theory than proved fact. Will update later. Consider this food for thought rather than a blueprint.
My goal is a fast PC, but speed isn't my highest priority. More importantly, I want a robust, reliable system that's as close to silent as practical. I'm interested in Ivy Bridge because the new chips draw less power. Although low power is often promoted as a "green" attribute, I'd say the "green" factor is irrelevant here. You'll save more energy by driving one mile less per week than you'll save by choosing a component that draws a few watts less. As far as I'm concerned, the main appeal of low power is low heat, which means less need for cooling, which means slow fans, which means your system is quieter. Also, lower heat reduces the likelihood of component failure.
So here's the breakdown. First, you'll need a case and a power supply. I'm pairing an Antec Sonata Series SOLO II Black ATX Mid Tower Computer Case with a SeaSonic SS-400FL2 Active PFC F3 400W 80 PLUS Platinum Fanless ATX12V / EPS12V Power Supply (or if you want a few more watts of power (which you probably don't need), a Seasonic ATX 460 Active PFC F3 80 PLUS Platinum Fanless ATX12V/EPS12V Power Supply SS-460FL2. There are various "quiet" cases, but this one works particularly well with the fanless (silent!) power supplies because it mounts the power supply at the top, and has a vent for the heat to rise. So this is one of the few cases that is actually built for optimal use of a fanless power supply. And Seasonic is a reliable brand; I'm willing to pay a premium price for their products.
For the heart of the PC, I'm going with Intel components. I definitely want a Z77 motherboard; there are plenty of good choices, but I'll play it (in theory) safe with an Intel Desktop Motherboard LGA1155 DDR3 1333 ATX - BOXDZ77BH55K.
For the CPU, I'm looking at the maximum power dissipation numbers for the quad-core processors. There are 3 levels that are (or will) be available in the Ivy Bridge quad-core line: 77 watts, 65 watts, and 45 watts. I figure the 65 watt CPU is probably my sweet spot, in that it's fast enough but should have little tendency to overheat. There are two 65-watt choices as I'm writing this (more will be coming), Intel Core i7-3770S Quad-Core Processor 3.1 GHz 8 MB Cache LGA 1155 - BX80637I73770S and Intel Core i5-3450S Quad-Core Processor 2.8 GHz 6 MB Cache LGA 1155 - BX80637I53450S. I'm getting the first.
The stock heatsink included with the CPU will do the job, but I want something quieter. There are plenty of good choices, but I've got the Noctua NH-D14 6 Dual Heatpipe with 140mm/120mm Dual SSO Bearing Fans CPU Cooler. Strictly speaking, this huge heatsink is overkill, and can handle a much hotter CPU than I'll have here. But I figure this allows for a slower (and thus quieter) fan. So I'll cool the heatsink with the 140mm fan alone, set to its minimum speed, and see how cool that runs.
I think I'll add a couple of extra case fans to the front. I'm looking at the Noctua NF-S12B ULN 120 x 25mm Fan (Ultra Low Noise - 500/700 RPM), which should be inaudible if I believe the claims.
(In sum, I'm thinking that I'll keep a slow, steady, quiet flow of air through the case. This should be enough to keep heat from building up, given the low power draw of the components. That's the theory, anyway.)
The motherboard and CPU already includes a decent basic video connection. If you have no particular interest in games or graphics, the on-board video is probably fine for your purposes. If you're a graphics maven, you'll want a powerful video card, which will have a fan that will add to the noise. I think I'd like a graphics upgrade but I don't want to add a fan. Here's a compromise, a decent (but by no means spectacular) graphics card that has no fan. Sapphire Radeon Ultimate HD 7750 1GB DDR5 HDMI/DVI-I/DP PCI-Express Graphics Card 11202-03-40G.
An SSD would be nice if you can afford it. The brands I'd trust most are Intel and maybe Samsung. Examples are an Intel 330 Series Solid-State Drive 120 GB SATA 6 Gb/s 2.5-Inch - SSDSC2CT120A3K5 or Intel 320 Series 160 GB SATA 3.0 Gb-s 2.5-Inch Solid-State Drive or Samsung 830 - Series MZ-7PC256N/AM 256 GB 2.5 Inch SATA III MLC Internal SSD Laptop Kit with Norton Ghost 15. I chose an Intel 320; it's an older design, but I respect its track record.
A large hard disk to store data makes a good complement to a smaller, faster SSD. I'm partial to the Western Digital "Green" lines, because they're cool and quiet (but be aware that these are not as fast as some others). I bought WD Green 2 TB Desktop Hard Drive: 3.5 Inch, SATA III, 64 MB Cache - WD20EARX.
(For greater data security, I set up a RAID 1 or RAID 5 array, so as to provide some protection against drive failure. Remember, hard drives won't last forever. In any case, back up your essential data!)
If you want to measure how much power your system draws, get a P3 P4400 Kill A Watt Electricity Usage Monitor. I'm guessing that the system I'm describing here will idle at 60 watts or so, and may go above 100 when active. We'll see.
I have nothing to say at this time about a DVD or Blu-Ray drive; get whatever is recommended. They're certainly cheap enough.