Dedicated hashcat brain server
If I wanted to deploy a dedicated hashcat brain server, are there any recommended system specifications?

Assuming that I don't want to deploy a virtual machine, could an Intel N3450 Mini PC (usually under $200 on Amazon) be enough to do the job or would that not have enough RAM for large workloads?
The amount of RAM you'll need is highly variable, depending on the attacks you'll be carrying out, with factors like:

* Whether all systems will be on the same LAN, vs operating over a WAN connection (faster connection means more candidates, so more RAM needed)
* Whether the hashes are fast or slow (fast hashes means more candidates, so more RAM needed)
* Whether you'll be using --brain-client-features of passwords, positions, or both (passwords = candidates, so this will consume much more RAM than positions alone)
* How many clients will be participating (more clients means more candidates, so more RAM needed)

And note that these variables are interrelated - for example, if many clients are operating over a WAN connection, they'll be competing for bandwidth, which might become a bottleneck that would slow down RAM consumption, etc.

You could take the "worst" case (fast hashes, fast LAN speeds, --brain-client-features 1 or 3), run a particular attack, and calculate the relationship between your particular keyspace and the resulting RAM consumption.

In general, having a lot of RAM available will leave your options open. In my limited testing so far, you don't have to have a super-fast CPU to run a good brain, but it seems to me that having 64GB of RAM would be pretty handy. Such a system would also enable some good processing of wordlists, etc. (In fact, I was eyeing some NUCs myself!)
This is what I was actually interested in understanding.  I wanted to understand if a dedicated brain server would require GPUs or is it fine to have a powerful CPU and bucketloads of ram?
Fair question. No GPU required for the brain, unless you want to also use it as a client at the same time.