Best video card for dual monitors using 800x600 resolution

you didn't provide information like what apps you run most of the time. at 800x600, you are probably running a web browser, email client and basic apps... nothing heavy.

Assuming that is true, almost any dual monitor graphics card with a nice processor and onboard ram will provide good service.

Here is an article that should help

http://www.techradar.com/us/news/computing-components/peripherals/the-complete-guide-to-multiple-monitors-1074313

I can see from the specifications on the motherboard you listed above - Asus P8Z77-V LK that not only does it have integrated graphics, you have multiple video connectors already available to you.

You shouldn't require an additional graphics card to do what you want.  It may be a matter of getting the right connectors to support your monitors. eg. DVI to VGA etc...

Integrated Graphics Processor
Multi-VGA output support : HDMI/DVI/RGB/DisplayPort ports
- Supports HDMI with max. resolution 1920 x 1200 @ 60 Hz
- Supports DVI with max. resolution 1920 x 1200 @ 60 Hz
- Supports RGB with max. resolution 2048 x 1536 @ 75 Hz
- Supports DisplayPort with max. resolution 2560 x 1600 @ 60 Hz
Maximum shared memory of 1696 MB
Supports Intel® HD Graphics

Here is the CPU I am using:

http://www.newegg.com/Product/Product.aspx?Item=N82E16819116504

That link is to your processor.

Sorry, I read it wrong

That's an Ivy Bridge with HD4000 => it will support 3 displays at once, so you do NOT need a video card to do what you want :-)

Thanks!