The Catalyst drivers have a few issues with video playback. I suggest using the open source drivers (radeon), they should work much better. The downside is slower 3D performance, but you won't need much of that for a HTPC, right?
Any recent distribution would work, but fedora usually has the latest versions of radeon. mplayer with xv output should work for most video files. For high-bitrate HD movies, you'll need either GPU decoding (not available on your HD2600) or the experimental mplayer-mt (so decoding is done on both CPU cores).