Here's what I would suggest for your usage:
(I have put a bit of cash towards quietness in this build, if quietness isn't an issue you could make it ~$50-100 cheaper)
AMD FX-8120 - $199.99
This is because I suspect the 8 cores may trump an i5 for running multiple VM's and that kind of thing.
ASUS M5A88-M AM3+ - $99.99
This is one of the cheaper AM3+ boards but should be fine as you shouldn't need anything fancy. As with most AM3+ boards though (especially the cheaper ones), there's a strong chance it could come with an earlier BIOS version which means you would have to buy a cheap AM3 Sempron and update the BIOS before using the FX chip. Another bonus of this board though, it is mATX but still has 4 sockets for RAM as well as USB 3 and SATA 3.
CORSAIR XMS3 16GB (4 x 4GB) - $79.99
As I said before, VM's are really RAM hungry so you are one of the few people that can justify 16GB it seems
PowerColor Go! Green AX5450 HD 5450 1GB - $29.99
This really is all you need for 2 monitors, this is passively cooled too which is always nice for silence.
Samsung 830 128GB SSD - $199.99
I have this drive myself and it really is the best around in terms of a good mix of performance and reliability. One of the fastest drives around while still being very reliable. Looks awesome too
Seagate Barracuda 500GB - $84.99
Nice quiet and reliable drive, it's no slouch in terms of speed either so this should be a good option assuming 500GB is enough for storage.
SeaSonic SS-350ET 350W - $42.99
This build shouldn't even pull 200W so 350W really is more than enough. Seasonic are also well known for reliability and silence. (This is OEM so you might need a power cable.)
Fractal Design Define Mini - $109.99
A tad expensive but is nice and small, well made and will really help for quietness. Not to mention the more subjective fact that it's beautiful
Scythe Shuriken CPU Cooler - $34.99
Most might think this is overkill but I wouldn't trust a 125W CPU on a stock cooler personally. For the sake of $35 this gives you peace of mind and will be far quieter than the stock cooler.
ASUS DVD Burner - $18.99
Standard DVD Burner for installing your OS etc. This one just happens to have free shipping at the moment.
Total - $901.90 (No rebates)
This comes in your budget nicely and with 8 cores and 16GB of RAM it should cope with your heavy multi tasking nicely. In terms of quietness, this should be nearly inaudible too.
If you are prepared to put up with something a bit more noisy you could drop the cooler and get a cheaper case and PSU to save $100 as well.
Hope this helps