Headless is a blanket term for anything without a GUI.
In that sense you intend to not use a monitor, mouse and keyboard and just have an SSH server running. I’m not going to go into that specially – but I will talk a little about hardware.
There are a few options I personally think that fit the above criteria pi 3rd generation is great choice. Not as pokey as the gen 4 but still great. 512mb ram and quad core ARM something something – it will run nice and quickly. But it’s still quite pricey if you get the default model B plus so here’s the money saving tip.
The model A plus is actually pretty much the same as the model B plus but with less stuff. Less USB (use a hub), no ethernet (use a hat) it’s also smaller in a nice square foot print which will make you laugh every time you look at it, “that’s a computer! No way…” And although that’s true for the model B plus it’s even more so for the model A plus.
The best bit, the model A plus is a fraction of the price.
It might struggle to run a desktop but you can always use raspberry pi OS lite which fixes that because it’s shell only.
Lastly for my application I will be sticking a battery onto it and running a TCP server to run an RC car with pi onboard, the a plus’s size is what sold it to me but I have to say this is a brilliant little computer worth your time.
Regards, there is no raspberry emoji 🍓