My setup was about 500 USD if I had to guess:
Used i5 9500 (mainly for QSV but you can use any modern CPU as long as the iGPU is relatively recent)
32GB RAM (more RAM = more cache for file IO)
4TB HDD
256GB NVME boot drive (recycled from my steamdeck)
Node 804 case.
TrueNAS SCALE for the OS.
I'd recommend to get double or even triple the drives I did, maybe 3x 2TB or 3x 1TB depending on your budget. Only because that unlocks RaidZ1/RaidZ2 which can give you better RW speed and redundancy should anything go splat, and you can't retroactively convert your drive into a Z1/Z2 pool without manually transferring the data later which might take a looooong time for you.
I dont think my route was the cheapest: IMO youd do better going AMD even despite the poorer support for HW transcode only because the motherboards are insanely expensive and hard to find, whereas that money couldve given me a better CPU and later you can add an intel iGPU if you're really struggling.