A quick primer on DVI:
There are two distinctions to look for: SL vs. DL, and DVI-D vs. DVI-I.
The first, single- and dual-link, designates the bandwidth of the connector. In general, you need dual link DVI to transmit resolutions above 1080p 60Hz. In other words, this doesn't matter to you.
The DVI-D vs. DVI-I distinction is a bit more muddled, but in general only applies to graphics cards, not monitors. D stands for Digital, while I stands for Integrated, IIRC. The difference is that DVI-D can transmit only a digital (actual DVI) signal, while DVI-I can alternately transmit a VGA signal instead, through a passive DVI-VGA adapter. Technically, there exists DVI-A (analog) as well, but I've never seen an actual DVI-A cable (as all of its necessary pins are there in SL-DVI).
Again, this flexibility applies to graphics cards, not monitors, or more generally signal sources, not sinks. If your monitor (sink) has a DVI input, it's a digital input, and as long as one of the modes supported by your graphics card (source) is a digital DVI signal, you're fine. And as
all DVI ports support digital DVI signals (duh), you're fine. HDMI or DisplayPort is also relatively easily adapted to DVI.
A monitor with a resolution as low as the one you're talking about only needs single-link DVI, and DVI on monitors is always DVI-D (digital). Just get a generic cheapo DVI cable at the length you need/want. Pretty much anything should work.
This article has some helpful illustrations. Any of the four top images is okay for your use.