"AI" is a very broad term. Back when I went to university, my AI course started out with Wumpus World. While this is an extremely simple problem, it's still considered "AI".
The enemies in computer games that are controlled by the computer are also considered "AI".
Machine learning algorithms, like recommender algorithms, and image recognition are also considered "AI"
LLMs like ChatGPT and Claude are also "AI"
None of these things are conscious, self aware or intelligent, yet they are part of the field called "AI".
These are however not "AGI" (Artificial General Intelligence). AGI is when the machine becomes conscious, and self aware. This is the scenario that all the sci-fi movies portray. We are still very far away from this stage.
As long as it's capable of booting into Linux, then you can start building a homelab...
Initially I had a 2-bay Synology NAS, and a Raspberry Pi 3B... It was very modest, but enough to stream media to my TV and run a bunch of different stuff in docker containers.
In my house, computer hardware is handed down. I buy something to upgrade my desktop, and whatever falls off that machine is handed down to my wife or my daughter's machines, then finally it's handed down to the server.
At some point my old Core i7-920 ended up in the server. This was plenty to upgrade the server to running Kubernetes with even more stuff, and even software transcoding some media for streaming. Running BTRFS gave me the flexibility to add various used disks over time.
At some point the CPU went bad, so I bought an upgrade for my desktop, and handed my old CPU donown the can, which released an Intel Core i5-2400F for the server. At this point storage and memory started to become the main limiting factor, so I added a PCI SAS card in IT mode to add more disks.
As this point my wife needed a faster CPU, so I bought a newer used CPU for her, and her old Intel Core i7-3770 was handed down to the server. That gave quite a boost in raw CPU power.
I ended up with a spare Intel Core i5-7600 because the first motherboard I bought for my wife was dead, so I looked up and found that for very cheap I could buy a motherboard to match, so I upgraded the server which opened up proper hardware transcoding.
I have since added 2 Intel NUCs to have a highly available control plane for my cluster.
This is where my server is at right now, and it's way beyond sufficient for the media streaming, photo library, various game servers, a lot of self-hosted smart home stuff, and all sorts of other random bits and pieces I want to run.
My suggestion would be to start out by finding the cheapest possible option, and then learn what your needs are.
What do you want your server to do? What software do you want to run? What hardware do you want to connect to it? All of this will evolve as you start using your server more and more, and you will learn what you need to buy to achieve what you want to.