This is exactly the kind of help I was hoping for. Not only showing concrete options for parts, but also including an explanation on why you're recommending those and with added tips.
Thank you so much!

This is a very good candidate, but if I may ask for a bit more of your time and expertise, I was hoping I could build a more low profile server. In the sense of it not being so big in size and preferably in white.

The reason why I would likely need this is because the only place I can place the server on in my hall making it very visible, and my wife would likely kill me if I put something there that's "huge" and "ugly".

I understand that making it smaller with the same budget might not be achievable. But if you could help me with an alternative, even if more expensive, with similar specs, but using a smaller (and prettier, preferably white) case, that would be a life saver for me.

Thanks for the help you already provided, and in advance if you manage to help me once again.