I know it's been done before, but a Weighted Companion Cube would work.
It can be small.
It definitely was built with graphics (gaming) in mind.
I made a couple of sketches for the internal design.
As shown, the cube will be cooled by a fan at the bottom.
The Ion board might be cooled better if it is mounted upside down so it faces the fan.
A 32 gb Solid State hard drive would be enough, and the physical size should be minimal.
The DVD Drive is at the top. If it could open upwards, like a Gamecube and some DVD players, that would be awesome. For reference:
The next sketch shows a little more about ventilation. More vents may be needed.
Now, just a companion cube would be kind of lame. It needs a turret. The turret should contain a bluetooth laser virtual keyboard, with the emitter on the keyboard housed in the laser sight of the turret.
For a mouse, any bluetooth mouse painted with an Aperture Science theme would do.
And now for a price tally. Everything is overestimated, I hope.
USB Bluetooth adapter, if bluetooth isn't available by default- $20
Portal - $10 or 15
Bluetooth Laser Virtual Keyboard- $200
Bluetooth mouse - $40
32 gb internal Solid State hard drive - $100
DVD Drive (Preferably top opening) - $50
120 mm fan - $5 to 10
Power- Preferably an external power brick. No idea what the cost could be.
That leaves about $100 for any parts I might have skipped, including paints and case materials.
I don't know whether plexiglass, plastics, or metal would be best for the case. I leave it entirely in your hands.