I would recommend a passively cooled Radeon 9550 or 9600 for you if you would consider ATI cards. As it is, my main advice is to look for a passively cooled card, as that's one less fan to make noise in your case and fail. The 6800 actually uses less power than a 9800P, so that's a bonus in terms of a cooler case and less-stressed power supply. Any current video card will look good playing DVDs, so that's not really an issue. If you can afford it, though, I'd get a passively-cooled 6800 over an actively-cooled 6600GT: it'll be quieter and faster in games. For your use, either card is sheer overkill. The vast majority of the cost of either card goes to features you won't use: namely, the 3D core and lots of fast memory, both of which are essential to 3D gaming. You could always just buy two el-cheapo PCI cards (or an AGP and a PCI card) with a single DVI output each and drive your LCDs just as well.
One more note, tho I don't know how big of a deal it is: both ExtremeTech and TomsHardware have conducted DVI Compliance tests showing that nVidia's integrated TDMS (read: digital DVI output) is subpar to ATi's at above 1280x1024. Now, I don't think this translates into a glaringly or even noticably inferior picture, but you might want to know. In any case, I don't think nV has two TDMS transmitters integrated on-die, so at least one of the DVI outputs on a dual-DVI card (which would be a Silicon Image--not nV--TDMS) should be fine (at least, according to an oscillosope) at high res.
In short, the simplest--but not necessarily the cheapest--solution would be to buy a passively-cooled nVidia card with dual DVI outputs. On the plus side, a passively-cooled 6800 should hold its resale value pretty well, so you could always sell it later to buy a lower-powered, more mainstream card once dual DVI becomes more mainstream.