I can only give you my personal experience on 4 machines with ATI GPUs: I used to have an Acer Ferrari 3000 laptop (bought 2003) with ATI Radeon 9200 GPU. That worked with the open-source xf86-video-ati driver (the GPU is not supported by the closed-source FGLRX driver). I have a Gateway Solo 9300 laptop (bought 2000) with an ATI Mobility-P GPU and that works with the open-source xf86-video-ati driver (it's not supported by the closed-source FGLRX driver). I have an Acer TravelMate 8215WLMi laptop (bought 2006) with ATI Mobility Radeon X1600 GPU which works with the open-source driver (it's no longer supported by the closed-source driver since March 2009, but did until version 9.2). And, finally, I have a badged Compal NBLB2 laptop (bought 2010) with ATI Mobility Radeon HD 5650 GPU which works (very well) with the closed-source FGLRX drivers to date.
I suggest you google your intended GPU model along with keywords such as "ati-drivers", "fglrx", "linux", "gentoo" etc. to see what comes up. Also search through the SL Forums as there have been several threads about AMD/ATI and NVIDIA GPUs over the last few years. You can also have a look at the AMD release notes for the latest FGLRX driver (a.k.a. Catalyst driver for Linux): Release Notes Catalyst 11.2
Phoronix Web site article: AMD Catalyst 11.2 Linux Driver Released
, which confirms that the HD 6800 Series is now supported officially.