This is very much the wrong forum for my answer... but you might be a lot better off with a Raspberry Pi or similar. These things can handle 4K video decoding and scaling in hardware, use much less power and output to HDMI natively.
That being said, I am sometimes running an old Core Duo notebook (1.5 GHz or so, 2 GB RAM) with integrated Intel graphics and Linux. VLC handles MP4 at 1080p fine, although it struggles with high bitrate files. Network streaming also puts a surprisingly heavy load on the CPU, causing decoding performance to drop. Any in-browser entertainment (Youtube) is barely acceptable at 720p and cannot keep up at 1080p due to the network. Also, forget about any modern encoding (H.265, VP9 or similar).
Another data point: I've used a VIA C7 (1 GHz) subnotebook, and it could handle 720p really well with hardware decoding (I don't think the hardware supported 1080p decoding at all.) However, the video would display in front of everything else, including the player controls. It wasn't the best experience, but it worked.
To summarize: You probably won't be happy with your idea.