I highly recommend you try proxmox to get the most potential out of you system. Basically can run many services and vm with little overhead, dynamically sharing the specs.

Now about those specs… what everybody else said really but heres some pointers:

You don’t need a big dedicated gpu unless your doing something that explicitly demands it. They are tricky to setup with virtual machines also.

If you plan on running a minecraft server i recommend at least 8gb ram. Most will probably run fine on 4. You can probably run quite a few things on 8gb but ram is cheap and its nice to have some extra room.

For cpu, the more things you do the More sense it makes to have more cores. If you plan on buying then amd ryzen x y z is you best option where.

X is the number you want higher Y is a number you should not care about as much Z is potentialy the letter “G” for graphics, they are often more expensive. Get them anyway because now you dont need a dedicated gpu (and even if you already own a gpu. Trust me you will thank me if that one ever has issues)

If you really want me to draw you something decent up that will give you plenty of freedom to experiment.

Ryzen 7 … G, 32gb ram. Small ssd for os. xTB of performence HDD ideally configured as some raid in proxmox.

It still cannot be said often enough that a (well cared for) second hand unlabeled laptop running ubuntu is all what most people need when they start pondering about home servers.

Go wuth what you have. Old laptop? Works! Old desktop? Also works! Old android phone? Might work! (VM/terminal)

If you have a device that can run Linux, start with that. Once you get some usage you can understand if you need an upgrade, and what kind. Maybe you will findout that this old laptop that you had works perfectly and you can sace money on buying a server.

A raspberry pi 4 or 5 and some fast USB 3 hard drives.

Why would raspberry pi’s be expensive but the hardware to build a server be any cheaper?

The minimum spec is whatever e-waste you can find that still powers on.

My home server has an i3-4160, 10 gigabytes of mis-matched RAM, a ten-year-old 240 GB SSD with 36000 hours on it, and three 1 TB hard drives in a RAID5 array each with ~25000 power-on hours. It runs Proxmox on the metal with a virtualized OPNsense, Nextcloud, and Jellyfin server (plus smaller services). Jank levels are high, but not fatal, and it was mostly free.

I run about thirty services off of an old Dell workstation that I “acquired” from my last corporate job. That includes a full Servarr stack. I’m pretty sure whatever you have will probably do the trick.

This specifically depends on what you want to run.

I’d say grab any unused PC in your home or off the street and it’ll work. Raspberry Pi are good for low wattage so it’s not expensive to run 24/7/365.

The electricity savings would pay for itself over time vs a 10 year old random desktop.

If you aren’t planning on running a media server go for a old desktop or laptop (with Ethernet port). Your bottleneck will be your network speed 9 time out of 10. Also use a firewall and a anti scrapper (ex: Anubis) to avoid wasting resources.

The things I paid attention to was

USB3 - you need this otherwise connecting external drives will be a joke Motherboard needs to accept up to 32 GB of RAM. Mine currently has only 8 but knowing I can upgrade is nice.
Quiet - must be silent when idle.
CPUs of less than 8th? gen will suck at video transcoding due to lacking certain capabilities. Important if running jellyfin, etc.

The beauty of self hosting is it’s all about your individual circumstances so you priorities and acceptable tradeoffs will differ.

A repurposed old PC with something like yunohost, generic Debian, or some lightweight Linux will probably get you what you need.

It heavily depends on what programs you want to run.

This depends entirely on what you want to run. A pihole needs vastly different resources than for example offering jellyfin to 20 simultaneous users. Both can be hosted at home.

If the size and low power consumption of the Pi are what appeal to you, you can try a getting a used thin client. Lots of suggestions and specs here: http://parkytowers.me.uk/

What are you intending to run on this server?

• If it is just PiHole, you can basically get the weakest computer you can find.

• If you want lots of storage space, you will need to make sure you have a case and motherboard that will accommodate the drives.

• If you are running encryption on those drives as well, you will need a CPU more powerful than what comes in a Pi, but nothing crazy.

• If you are running lots and lots of VMs, you will want lots of RAM. A linux VM will use maybe a few GB each depending on what software each is running internally, a windows vm will use a bit more.

• If you are doing AI workloads, you will need a graphics card.

I’m running an old Igel M340C thin client to run a lot of stuff, from Jellyfin to AdguardHome. Perfectly enough.

A computer. Seriously that’s it. Of course depends on your use case (media servers usually need more than a web host for example)