I'm going to go out on a limb here and say that the Arduino isn't really a good match for this sort of application. The big shortcoming is that it doesn't have enough memory to hold a "modern" webpage during the "rendering" that is required to format the page for a screen, even if the screen is relatively smart. (unless it's actually a very small web page.) Arduino is also not well equipped for "very fast" networking (though the need for fast networking may be somewhat overstated unless you're doing multimedia type things (overstated in general, not just for your project.)
Something like a beagleboard (http://www.beagleboard.org) or even an old or small PC clone would work better (though it might cease to be an interesting project at that point.)