I actually just set this up for myself about 2 months ago. This year I built myself a new gaming PC, and the entirety of my old PC was just lying around. I had a mobo and processor, 16 GB RAM, a 500 GB SSD and the case and PSU. I wanted a dedicated Minecraft server that I could run a modpack on so my brother and I wouldn't have to pay (most server hosting doesn't even go up to 16 GB RAM). I wiped the SSD and installed Ubuntu server (didn't want to pay for Windows license) on it which I had to completely learn how to use, and ultimately I was successful. During the build, I just used the integrated graphics (Intel processor) but now I don't even have an HDMI cord plugged in...I just SSH into the server from my gaming PC or phone to reboot or whatever. Since I already had the components, it was completely free besides the time it took to learn how, and so far I've loaded like 4 different modpacks on it trying to find a good one and each one gets easier to configure than the last. I've only saved money since I put it together.

tl;dr I HIGHLY recommend setting up a personal server. It has a learning curve but it is beyond worth it. I don't think you even need 1TB and if you use Ubuntu server you only need integrated graphics because it's command line only. I do recommend a beefy amount of RAM for sure.