Hardware
Ansible-NAS will run against any Ubuntu box, a Raspberry Pi 4, or even a VM if you're just testing things out. The hardware you pick for Ansible-NAS depends largely on what you intend to do with your server - and is very much a "how long is a piece of string" type question.
The homeserver Reddit has lots of good information.
Questions To Think About
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What will be taxing the CPU(s) on your Ansible-NAS box? Are you intending to transcode video? How many users will be hitting it?
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How many applications do you intend to run in parallel? How much memory do these applications require?
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Are you going to run the ZFS file system?
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What are you intending to store on your Ansible-NAS? Is it data you can download again, or is it important to you that you don't lose it? Do you need mirrored disks?
HP Microserver
Ansible-NAS development is tested against an HP Microserver N54L, with 16GB of memory, a 120GB SSD for the OS and 5x4TB WD Red NAS drives for storage. It works great :-)
This is obviously not the only solution but a reasonable one if you just want a single box to buy. Many different models are available on eBay at varying prices.