What are the rakes when assembling a server from desktop hardware in a 19" case?

Question

Computers

Good afternoon.
For some amateur project, I'm building a server (with a specific "stuffing").
It will be located in the DC (I discussed it with the DC, they don’t care, the main thing is that it’s 19 inches)
It will not be used very actively, so I consider reliability not very critical.
two requirements:
- have something like ipmi
- be as cheap as possible (it will be rarely used, but at these moments it will be loaded to the maximum)
(important: the dediks are not suitable, I consider used ones as an extreme option)
With "IPMI" everything pretty good: Intel's Q-series chipsets, supported by the IntelvPro technology processor, allow you to connect even to a turned off PC via VNC or its equivalent.
The content is something like this (socket numbers, I don’t indicate processor details, because it’s not interesting and is of little relevance):
- Used case, used PSU (2 months)
- Mini-Atx mat. board
- CPU i5 or i7, but here the question is with a radiator and a cooler, which are included in 1U (how to look for them?)
- memory sticks two by eight (without ECC, because there are no critical applications)
- two 2, 5 SATA disks in a soft raid, one 32G SSD (let it be so clean)
Questions
- how to look for a cooler that will fit into 1U (maybe it's called something, but I don't know how)
- if anyone has experience using Intel AMT, can you tell me if it can be an alternative to IPMI in servers?
There will be debian on the piece of iron, but this is of little relevance.
Thanks in advance.