I've used the cheapest celeron nuc for this. Has built in IR, just add a usb drive / laptop drive and memory. Not much more expensive than a dedicated box here in Aus, and much faster.
At this price point you'd probably be better served by an Intel Compute Stick, although the current ones only do 1080p HDMI 1.4a output. Rumor is that the next generation ones might do 4K though.