I wouldn't go beyond a Pentium.
Pentium G2120 (dual core) - $95
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
ASRock B75M-DGS MicroATX mobo- $55
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
G.Skill ECO Series 2x2GB DDR3-1600 RAM Kit -$40
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
SAMSUNG 830 Series 128GB SSD - $109
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
PC Power and Cooling Silencer MK III 400W Modular PSU - $70 ($50 with MIR)
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
Fractal Design Arc Midi case- $70
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
ASUS DRW-24B1ST/BLK/B/AS Black SATA 24X DVD Burner - $20
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
Cost without the OS: $459 (and no MIR)
Cost with Win 7 HP SP 1 @ $100: $559 (and no MIR)
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
Alternatives:
SeaSonic SS-300ET Bronze 300W PSU -$40
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
COOLER MASTER Silencio 450 - $70
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
Notes:
1. You won't need the 400W PSU from a power point of view. It's just modular. If you don't care about that, go for the SeaSonic.
2. The Silencio 450 throws in a SD card reader as well, if that's important. But otherwise, the Fractal case seems to be better (from the newegg reviews). Could have gone cheaper on the case, i just wanted to throw in USB 3.0, and a case that looked non-gamer.
3. Don't know if you'll find a better deal on the OS, or if you want Win 8 for some reason. But for win 7, stick to Home Premium.
4. The mobo only has one on-board fan header, but the Fractal case has a fan controller, apparently. You can obviously hook the fans to molex connectors directly.
5. You may want to look at the -T model pentiums as well, like the G2100T (not available on newegg) or the older G860T/G645T/G640T/G630T/G620T without a major hit in performance, though the idle power consumption should be very similar, and this system will hardly ever be at full load. But i still think the G2120 is a better idea, fastest Pentium there is, and more efficient than the 65w G870.
6. You could shave a few bucks off on the RAM by using regular 1.5v sticks.
Finally what i tried to do with the build was:
1. Lowest power consumption without sacrificing too much performance.
2. Fast boot and application loading, along with reliability (Samsung's SSD)
3. Good silent cooling
4. Maximum usability from things like USB 3.0.
5. Trimming unnecessary features like 4 RAM slots
6. A clean build (modular PSU).
Cheers