do you think that's a great idea? i mean its a small pc which is great for cabinets
Why is a small PC great for cabinets?
There are cubic feet of empty space available.
For a cab, I'd prefer to use something more standard so I can swap parts and upgrade later.
I bought an alpha to use as a console for the living room.
I haven't got around to installing any emulators on it though.

Processor speed is king in emulation. You can't just say Alpha or i3 or i5.
They make faster and slower ones. Ghz matter.
I got a refurb one with an i3-4170 Processor (up to 3.7 GHz) with a wireless xbox controller for $363 before tax.
(probably about as cheap as I could have built a similar spec PC for by the time I bought the OS)