This will be easiest to fit the $500 budget (without HDD)
This will be cheapest depending on what we can find in your market for mini-ITX
This will be the most expensive option as the choices of server boards in mini-ITX is limited. Here's a few :
https://www.supermicro.com/ResourceApps/MB_matrix.aspx
Look for the mini-ITX form factor. There are quite a few in the X11(latest generation) and in the older generation (X10, X9, X8). But many of those boards will not be available easily in the market or even if they are they might cost a lot of money and be out of your budget.
This is not possible. The Node304 does not offer a lot of space beyond the mini-ITX dimensions. If you are bent upon Node 304, you will need to stay with a mini-ITX board