ATI is no longer. Its AMD now.
If you're insisting on using 10.6.8, you're going to be locked into graphics card hell. The AMD Radeon 6870 flashing utilities require 10.7, and while the card will boot in 10.6.8, the performance is glitchy at best, with quicktime often refusing to play, where as 10.7+ its fine.
10.8 never gave me any issues on my 2008 Mac Pro, and 10.9 seems to run better than any of the previous iterations of OS X on it. Any instability is likely due to a software problem, (be old kexts looming in your library or other evil glibblies).
Please please please, don't take this the wrong way but I get the sense that you may not feel comfortable flashing your own video card, so you're best bet is to look for either pre-flashed cards or buying used OEM video cards like the GeForce 8800 GT.