Currently I'm running Raspbian but I'm willing to install any version of Linux. I just need the Pi as a dedicated browser opening one internal site with images. Works great with Midori and Chromium but image transitions are very sluggish.
I have been playing with this and found the best I could get was Firefox for Pi.
apt-get the following:
iceweaselthis is the browser
browser-plugin-gnashthis is for some limited video like YouTube
The few sites I loaded perform well. Video is pretty bad, but at low settings on the quality and some higher settings on the Pi it's not too bad. For larger sites it can be a bit sluggish. I was running at pretty much every setting and a memory split of up to 256. It won't likely stream movies or long YouTube videos, but for checking mail and general surfing it can support much more then the stock browsers.