Ok, at the risk of being shot down :roll:
I would think that the only cheap Amiga would be an Amiga based on what's available today: Intel hardware.
Let's face it, it's fast, available and relatively cheap.
I can build a reasonable dual-core Intel box for around 400-500 Euro's (without monitor/keyboard).
The only difficulty I see and that is a major one,
is the plethora of GFX cards, one of the reasons for the existence of DirectX. Also, chipsets have a tendency to "dissapear" after a while, leaving the question of support open.
Ok, now you can shoot me....(hiding away)