If you’ve got an old laptop lying around that might work for free, or get a cheap old ThinkPad (you can squash 3 drives into a T440p for example).

If you’ve got some old PC stuff lying around and maybe a case, an AM4 5600G or Intel 12000 or so system can be pretty cheap to fill out the missing bits, boom, NAS (just doing this myself, only needed a mobo, sweet, check the bios supports undervolting for power savings). Get some extra PCIe slots for a HBA card as you grow, maybe an old video card for transcode. Even 8G RAM should get you going.

Otherwise, second the second hand SFF.

Work out if you need transcode for the media server, that will limit your options to specific later CPUs.