That's twice what I'd spend on a first server when you're still figuring out what you need!
My first "server" was a 65€ second-hand laptop including shipping iirc, in ~2010 euros so say maybe 100€ now when taking inflation into account. I used that for a number of years and had a good idea of what I wanted from my next setup (which wasn't much heavier, but a little newer cpu wasn't amiss after 3 years). Don't think one needs to even go so far as 200$ for a "local Bandcamp archive" (static file storage) and serving that via some streaming webserver
Jellyfin docs do mention "Not having a GPU is NOT recommended for Jellyfin, as video transcoding on the CPU is very performance demanding" but that's for on-the-fly video transcoding. If you transcode your videos to the desired format(s) upon import, or don't have any videos at all yet as in GP's case, it doesn't matter if the hardware is 20x slower. Worst case, you just watch that movie in source material quality: on a LAN you won't have network speed bottlenecks anyway, and transcoding on GPU is much more expensive (purchase + ongoing power costs) than the gigabit ethernet that you can already find by default on every laptop and router
My first "server" was a 65€ second-hand laptop including shipping iirc, in ~2010 euros so say maybe 100€ now when taking inflation into account. I used that for a number of years and had a good idea of what I wanted from my next setup (which wasn't much heavier, but a little newer cpu wasn't amiss after 3 years). Don't think one needs to even go so far as 200$ for a "local Bandcamp archive" (static file storage) and serving that via some streaming webserver
Jellyfin docs do mention "Not having a GPU is NOT recommended for Jellyfin, as video transcoding on the CPU is very performance demanding" but that's for on-the-fly video transcoding. If you transcode your videos to the desired format(s) upon import, or don't have any videos at all yet as in GP's case, it doesn't matter if the hardware is 20x slower. Worst case, you just watch that movie in source material quality: on a LAN you won't have network speed bottlenecks anyway, and transcoding on GPU is much more expensive (purchase + ongoing power costs) than the gigabit ethernet that you can already find by default on every laptop and router