Personally, if I were to build a system like this, it would be meant specifically to highlight the end of the DX9 era and the final days of AMD's supremacy over Intel (in other words, pre-Core 2 Duo).
In this case, I would stick with Pre-G80 graphics and the best CPU the board could handle (probably an Opteron 285 or 290?).
If you wanted something extremely weird and powerful but not necessarily the "best" cards from that era, you could get a pair of Geforce 7950GX2s (meaning, 4 way SLI with two cards). Technically, the 8800GTX was the best card from 2006, but its a DirectX 10 card and signified the start of the next era of GPUs, where as the 7900GTX and 7950GX2 signified the end of the DX9 era. The 79xx series were fantastic cards, they were just kind of lost to time since the 8800GTX came out later the same year (I actually had a 7900GTX, then a 7950GX THEN an 8800GTX all in 2006... lots of reselling). The 7950GX2 was extremely potent in games that could use it, but SLI was pretty iffy in those days... IMO, that makes it perfect for a "period" build, since the point is obviously not to play the games at the highest settings possible, or you'd just play them on a newer system.
When I build systems, they have a very specific era in mind. You could build a really really uninteresting "2007" system that is 100% period correct that has no special significance, or you could build one that contains the best AMD had to offer before Intel reclaimed the crown for the next 10 years and has the most powerful Pre-DX10 GPUs available.