As long as your server has no traffic to speak of, you might get away with this. I have the Pi, mplayer sucks, you have to use omxplayer, but that's ok.
You will have to readjust with nice to make the playback basically stop while httpd/mysql/php talk out. I frankly think this may be a bit much of a load. I don't even know if you can get all those programs for the arm. You can do playback; You can do browsing, but cpu load slows the process.
The browser situation is likely to be: You can get html, & ssl; java will be iced tea, and flash is out of the question - maybe a port of gnash. Youtube is doable with youtube-dl. TV replays (requiring flash) are not.
The Android offers '1cc' more power for less money so it looks the better bet. It also comes with a headstart on the java side.