For fully supported HDMI output (with 1920x1080 px = Full HD) you need at least AMD Radeon HD 5xxx (or above) or nVidia GT 2xx (or above).
Ideal are (TDP < 20W - passive cooling) HD 5450, HD 6450, GT 210, GT 710, GT 720.
Pentium Q8200 is more than sufficient.
4 GB DDR2 too.
My experience confirms, that for everything in full HD is enough Core 2 Duo 2,66+ GHz or Core Quad 2,33+ GHz (more powerful is of course not a fault :-).
Those CPUs can suprisingly with Libreelec handle common H265 HDR streams too (only up to full HD, of course - no 2k or 4k videos!).
1GB of system memory is fully suficient.
I am using Intel G31+E8400, 1GB DDR2 800, Radeon HD 5450 1GB DDR2 (complete consumption at the wall - idle 38W, burn 66W).
i am using it with small pico PSU (10 USD) and home-made 12V/8A switching supply (from spare part - 7 USD).
From second-hand components this can be completed very cheaply.
Now I am preparing new Librelec machine for friends - I bought old ITX board with Celeron 1037U (for 12 USD) with HDMI output.