Dear Juan,
Firstly, the AMD Radeon will probably not be usable with BEAGLE (there was an OpenCL implementation that may work if you can find OpenCL drivers for this board but I am not sure of the status of this). Secondly, the NVIDIA GT620 will work with BEAGLE. Looking at the specs:
http://www.geforce.com/hardware/desktop-gpus/geforce-gt-620/specifications
...it has 96 CUDA cores which is at the low-end for BEAGLE. This won't give you the sort of speed ups we reported in the papers. A rough guess is that this will be about 50% to 100% faster than the same analysis on the CPU (assuming that you have reasonably long sequences which is when you get the greatest benefit of GPUs.
It would be useful to get some benchmarks for some of these cards:
http://beast.bio.ed.ac.uk/Benchmarks
Andrew