I don't know what the money conversion is but the Acer Iconia (~$350 US)can do all that. I think someone recently did a movie test on one and it went 7+ hours with the screen at 50% brightness. It has a built in USB host port (external HDD connection), a Micro SD slot and an HDMI out (720p I think). The Clear.Fi software (the only software I mention that is ONLY on the Acer tablets) allows streaming from media shared on the network, it works well until you skip forward then the buffering is a bit slow if it's an HD video.
For controlling the PC, SplashTop is good, I have it and use it from my laptop and my Iconia, to control a desktop in the other room. That would fit those needs once you get the hang of it. I don't know if it's available where you are, the streamer app for the desktop is free, the version to connect to it from another Windows PC is free, the Android version is a pay app.
Acer has some updated models coming out, if a 10" tablet is too big, consider one of the 7" ones for less money.