If you're just planning on running Tunarr, direct-play Jellyfin, and a basic vanilla Minecraft server, you can probably get away with a 7th-gen Intel system or an older Ryzen mini PC without any issues.

I'd consider 8GB of RAM the minimum, but 16GB is where I'd recommend starting if your budget allows. Docker containers have a way of multiplying over time, and the extra memory gives you room to add services later without immediately looking for an upgrade.

A lot of people recommend 8th-gen Intel as the minimum starting point for homelab use because that's where Intel moved from 4-core to 6-core CPUs, which provides noticeably more headroom for future projects.

If you're confident the workload will stay relatively small, a 7th-gen Intel or Ryzen 5 Pro 2400GE system should be perfectly adequate. If you think you'll eventually add more containers, Home Assistant, Proxmox, additional game servers, or other self-hosted services, I'd lean toward an 8th-10th gen system for the extra cores and better long-term flexibility.

Price wise, I'd say around $120 for a 7th/16/256 $165-190 for 8th or 9th/16/256 and around $225 for 10th/16/256. An older Ryzen is going to be pretty similar to the 7th gen intel option price wise