About the power of the hardware, you don't need to worry too much. My NAS is a SBC with 6 ARM cores and 4GB or RAM. It run flawlessly all the services you've listed and more ! (Also, without transcoding for jellyfin).
I don't know if your budget includes Hard disks, but it should be plenty enough to get you an ready made NAS from Synology or other brands, that will give you an easy start with self-hosting.
If you want to go the DIY route. Then I recommend to build yourself a small computer from a Intel N100 motherboard, or the older J5040. From there you can install Open Media Vault, or otherwise the Linux distribution you are the most familiar with, and install Docker. You can check Linuxserver.io for many guides for spinning up docker containers for all of the services you've listed.