Unfortunately, the Ryzen 3 1200 -- as with most Ryzen chips -- doesn't have an integrated GPU. You would need to find some sort of video card and occupy your single PCIe slot.
A properly designed server motherboard would have a basic VGA port and an IPMI port, but buying those retail bumps up the price ridiculously. The NUC-style machines always have integrated video, sometimes really good (non-gaming) video, but offer only a single SATA port and a single M.2 slot.
It's just something I've found in a quick search. Current availability differs from the place to place but it's not a big broblem to find a CPU with G suffix.
My point - you can find a slightly older solution for less than $200, if you are okay to take some time to find it.
'Server' requirements are moot when we are talking about an extremly budget solution.
And honestly, as a person who extremely benefited from the existence of BMC/iLO/iDRAC - it is not that required for some cheap ass storage solution at home.
Like okay, you did wired another ether link for a BMC, installed OS aaaand... if something wrong with the box it is almost always requires to be near it to resolve the issue.
Edit: personally I have some low power GPUs laying around what can be used for the initial setup.
It was easier when you could fit some S3 Trio card on any machine, but still..
A properly designed server motherboard would have a basic VGA port and an IPMI port, but buying those retail bumps up the price ridiculously. The NUC-style machines always have integrated video, sometimes really good (non-gaming) video, but offer only a single SATA port and a single M.2 slot.