I plan on using the two displays I currently own -- a 30-inch display with a native resolution of 2560 x 1600 pixels, and the 24-incher at 1920 x 1200. Currently, they're connected to the DVI ports of an nvidia gpu installed in a (noisy) six-year old Dell tower.
I understand why you would want to upgrade to a cool and quiet new system. Dell has, mostly, made good systems. For a long time they did not appear to care about the noise that their systems made. Some new Dell computers are quiet.
Here's the list of mother boards I can choose from:
Oh wow. I think that you need to look up each of these boards and find out if they support dual-link DVI. An HDMI port or a DVI port on a low-end card (and most integrated video) is limited to 1920x1200 for a 60hz refresh rate.
Read more about Digital Visual Interface
The first thing to check is the product marketing material. Next, you would want to check the user manual PDF that you can download from the manufacture's web site. Finally, you could write an email to the manufacturer asking about the DVI port -- and the maximum resolution and refresh rate that the DVI port can support.
You can also check to see what resolutions are supported by the other connectors, like DisplayPort. You would then need to find a DisplayPort to DVI adapter. That might cost a lot of money, and might not work well.
In the end, you may be better served by a discrete add-in video processor like the AMD HD 6670, 6770, or 6850. Make sure you get a video card with GDDR5, as it will help you get the best performance.